CBSE Questions for Class 11 Engineering Physics Laws Of Motion Quiz 11 - MCQExams.com

If an object is in equilibrium, which of the following statements is not true?
  • The speed of the object remains constant.
  • The acceleration of the object is zero.
  • The net force acting on the object is zero
  • The object must be at rest.
  • There are at least two forces acting on the object.
Answer the question:
The diagram shows a uniform beam being used as a balance. The beam is pivoted at its centre.
A $$1.0\,N$$ weight is attached to one end of them. An empty pan weighing $$0.2\,N$$ is attached to the other end of beam.
How many $$0.1\,N$$ weights must be placed on the pan in order to balance the beam ?
1912286_c8bc18d085de4369a14a4d5e20cb5826.png
  • $$5$$
  • $$8$$
  • $$10$$
  • $$12$$
A block is freely sliding down from a vertical height $$4\ m$$ on a smooth inclined plane. The block reaches bottom of inclined plane then it describes vertical circle of radius $$1\ m$$ along smooth track. The ratio of normal reactions on the block while it is crossing lowest point and highest point of vertical circle is:
  • $$6 : 1$$
  • $$5 : 1$$
  • $$3 : 1$$
  • $$5 : 2$$
A mass m starting from A reaches B on a smooth track. On reaching B, if it pushes the track with a force equal to $$x$$ times its weight, then the correct relation is:

72704.jpg
  • $$H=\dfrac{xR}{2}$$
  • $$H=R$$
  • $$H=\dfrac{\left ( x+5 \right )}{2}R$$
  • $$H=\dfrac{\left ( x-1 \right )}{2}R$$
A vehicle is moving with a speed $$v$$ on a curved smooth road of width $$b$$ and radius $$R$$. For counteracting the centrifugal force on the vehicle, the difference in elevation required in between the outer and inner edges of the road is 

72700_2580dc087bea44168df76967a19fe59e.png
  • $$\dfrac{v^{2}b}{Rg}$$
  • $$\dfrac{vb}{Rg}$$
  • $$\dfrac{vb^{2}}{Rg}$$
  • $$\dfrac{vb}{R^{2}g}$$
A small block of mass $$m$$ is released from rest from point A inside a smooth hemisphere bowl of radius R, which is fixed on ground such that OA is horizontal. The ratio (x) of magnitude of centripetal force and normal reaction on the block at any point B varies with $$\theta$$ as:


72707_b5c01aa6a37c483c819de65f268021ea.png
The horizontal component $$N_{x}$$ and vertical component $$N_{y}$$ of the reaction at end P are given by:

43911_a5a2af67a76249fd953e8f54db828bad.png
  • $$\mathrm{N}_{\mathrm{x}}$$ $$=$$ $$1300\mathrm{N}, \mathrm{N}_{\mathrm{y}}=960\mathrm{N}$$
  • $$\mathrm{N}_{\mathrm{x}}=960\mathrm{N}, \mathrm{N}_{y}=140\mathrm{N}$$
  • $$\mathrm{N}_{\mathrm{x}}=960\mathrm{N}, \mathrm{N}_{\mathrm{y}}=960\mathrm{N}$$
  • $$\mathrm{N}_{\mathrm{x}}=1300\mathrm{N}, \mathrm{N}_{\mathrm{y}}=1300\mathrm{N}$$
Two persons $$P$$ and $$Q$$ of the same height are carrying a uniform beam of length $$3  m$$. If $$Q$$ is at one end, then the distance of $$P$$ from the other end such that $$P$$, $$Q$$ receive loads in the ratio $$5 : 3$$ is:
  • $$0.5\  m$$
  • $$0.6\  m$$
  • $$0.75\  m$$
  • $$1\  m$$
The tension in the string is:

43910_29f1c911d71b43e29db5d3f0b9618bd0.png
  • $$600$$ N
  • $$80$$ N
  • $$1200$$ N
  • $$800$$ N
The stick $$OA$$ rotates about a horizontal axis through $$O$$ with a constant counter clockwise velocity $$\omega =3$$ rad/sec. As it passes through the position $$\theta =0^{0},$$ a small mass $$m$$ is placed upon it at a radial distance $$r=0.5\ m$$. If the mass is observed to be slipping when $$\theta = 37^{o}$$ , then $$\mu$$ is :

72701.jpg
  • $$\dfrac{3}{16}$$
  • $$\dfrac{9}{16}$$
  • $$\dfrac{4}{9}$$
  • $$\dfrac{5}{9}$$
Two identical ladders are arranged as shown in the figure. Mass of each ladder is $$M$$ and length $$L$$. The system is in equilibrium. Find direction and magnitude of friction force acting at A or B.
42889_0edd8d8b417f4557adc0460c8c9bf5cb.jpg
  • $$ f=(\displaystyle \frac{M+m}{2})g\tan\theta$$ horizontally outwards
  • $$ f=(\displaystyle \frac{M+m}{2})g\cot\theta$$ horizontally inwards
  • $$ f=(\displaystyle \frac{M+m}{2})g\cos\theta$$ horizontally outwards
  • None of these.
An elastic string carrying a body of mass $$m$$ at one end extends by $$1.5\ cm$$. If the body rotates in vertical circle with critical velocity, the extension in the string at the lowest position is:
  • $$3.0\ cm$$
  • $$4.5\ cm$$
  • $$1.5\ cm$$
  • $$9.0\ cm$$
Which of the following statements for a rigid object undergoing pure translational motion are false?
  • If an object receives an impulse its kinetic energy must change.
  • An object's kinetic energy can change without the object changing momentum.
  • An object can receive a net impulse without any work being done on it.
  • A force may do work on an object without delivering any change in momentum.
A uniform of rod of length $$l$$ is placed symmetrically on two walls as shown in the figure. The rod is in equilibrium. If $$N_1$$ and $$N_2$$ are the normal forces exerted by the walls on the rod, then :

120010_4343ae2149fb4b10a4e4e39320e0916b.png
  • $$N_1 > N_2$$
  • $$N_1 < N_2$$
  • $$N_1 = N_2$$
  • $$N_1$$ and $$N_2$$ would be in the vertical directions $$N_1$$ $$N_2$$
An insect moves along a semi-circular transparent track of radius $$R$$, with a constant speed $$V_0$$. It starts from point O. A point source of light is fixed at the centre of the circle. What is the velocity of shadow of the insect on the surface at time $$t$$?

74716.jpg
  • $$V_{0}sin\left ( \dfrac{V_{0}t}{R} \right )$$
  • $$V_{0}cosec^{2}\left ( \dfrac{V_{0}t}{R} \right )$$
  • $$V_{0}sec^{2}\left ( \dfrac{R}{V_{0}t} \right )$$
  • $$V_{0}sec^{2}\left ( \dfrac{V_{0}t}{R} \right )$$
A uniform ladder of length $$5  m$$ is placed against the wall as shown in the figure. If coefficient of friction $$\mu $$ is the same for both the walls, what is the minimum value of $$\mu $$ for it not to slip ?

72810_5c95ceffe31b4e65aff9ebb568806737.png
  • $$\mu =\dfrac{1}{2}$$
  • $$\mu =\dfrac{1}{4}$$
  • $$\mu =\dfrac{1}{3}$$
  • $$\mu =\dfrac{1}{5}$$
Due to an impulse, the change in momentum of a body is $$1.8 \: kg \: m \: s^{1}$$. If the duration of the impulse is 0.2 s, then what is the force produced in it?
  • 9 N
  • 8 N
  • 7 N
  • 6 N
A very long uniform helix is made of thin metal wire. The axis of helix is vertical. A small bead begins to slide down the fixed helix starting from rest. Considering friction between bead and wire of helix to be non-zero, which of the following statements is/ are true as long as bead moves on helix.


72876.jpg
  • The speed of bead keeps on increasing.
  • The magnitude of frictional force on bead remains constant.
  • The speed of bead first increases and then remains constant.
  • The magnitude of frictional force increases and then remains constant.
A ladder of length l and mass m is placed against a smooth vertical wall, but the ground is not smooth. Coefficient of friction between the ground and the ladder is $$\mu$$. The angle $$\theta$$ at which the ladder will stay in equilibrium is:
  • $$\theta=tan^{-1} (\mu)$$
  • $$\theta=tan^{-1} (2\mu)$$
  • $$\theta=tan^{-1} (\frac {\mu}{2})$$
  • none of these
Two uniform boards, tied together with the help of a string, are balanced on a surface as shown in Fig. The coefficient of static friction between boards and surface is 0.The minimum value of $$\theta$$, for which this type of arrangement is possible is :

120027_a0b64d21103b4479ba016915b23e141b.png
  • $$30^o$$
  • $$45^o$$
  • $$37^o$$
  • It is not possible to have this type of balanced arrangement.
A vehicle is moving with a velocity $$v$$ on a curved road of width $$b$$ and radius of curvature $$R$$. For counteracting the centrifugal force on the vehicle, the difference in elevation required in between the outer and inner edge of the road is
  • $$\dfrac{v^2b}{Rg}$$
  • $$\dfrac{vb}{Rg}$$
  • $$\dfrac{vb^2}{Rg}$$
  • $$\dfrac{vb}{R^2g}$$

A stationary ball weighing $$0.25\  kg$$ acquires a speed of $$10 \ m/s$$ when hit by a hockey stick. The impulse imparted to the ball is:
  • $$2.5\  N s$$
  • $$2.0\  N s$$
  • $$1.5\  N s$$
  • $$0.5 \ N s$$
The reaction at hinge 1, before hinge 2 breaks, is:

120070_294f070dd3214479bd4d4c5b672c23a7.png
  • $$24 \ N$$
  • $$12 \ N$$
  • $$11 \ N$$
  • $$10 \ N$$
A pendulum was kept horizontal and released. Find the acceleration of the pendulum when it makes an angle $$ \theta $$ with the vertical.

134428_d53edfb0b74b403ebc2b1ccca7cfe9c9.png
  • $$ g\ \sqrt { 1+3\cos ^{ 2 }{ \theta } } $$
  • $$ g\ \sqrt { 1+3\sin ^{ 2 }{ \theta } } $$
  • $$ g\ \sin { \theta } $$
  • $$ 2g\ \cos { \theta } $$
What is the actual frictional force when the man has climbed $$1.0$$ m along the ladder?
  • $$360 N$$
  • $$171 N$$
  • $$900 N$$
  • $$740 N$$
A hemispherical bowl of raidus r is rotated about its axis of symmetry which is kept vertical. A small block is kept at a position where the radius makes an angle $$\theta$$ with the vertical. The block rotates with the bowl without any slipping. The friction coefficient between the  block and the bowl is $$\mu$$. The maximum speed for which the block will not slip
  • $$\displaystyle \left[\frac{g(\sin{\theta} -\mu \cos{\theta})}{r\sin{\theta}(\cos{\theta}+ \mu\sin{\theta})}\right]^{1/2}$$
  • $$\displaystyle \left[\frac{g(\sin{\theta} +\mu \cos{\theta})}{r\sin{\theta}(\cos{\theta}+ \mu\sin{\theta})}\right]^{1/2}$$
  • $$\displaystyle \left[\frac{g(\sin{\theta} +\mu \cos{\theta})}{r\sin{\theta}(\cos{\theta}- \mu\sin{\theta})}\right]^{1/2}$$
  • none of these
A particle P of mass m attached to vertical axis by two strings AP and BP of length l each. The separation AB=l. The point p rotates around the axis with an angular velocity $$\omega $$. the tension in two strings are $$ { T }_{ 1 }$$ and $$ { T }_{ 2 } $$
taut only if $$ \omega >\sqrt { \frac { 2g }{ l }  } $$

134954.jpg
  • $$ { T }_{ 1 }$$= $$ { T }_{ 2 }$$
  • $$ { T }_{ 1 }$$+ $$ { T }_{ 2 }$$=$$\cfrac{2}{\sqrt3}m\omega^2l $$
  • $$ { T }_{ 1 }$$- $$ { T }_{ 2 }$$=2mg
  • BP will remain
The spool shown in the figure is placed on a rough horizontal surface and has inner radius r and outer radius R. The angle $$\theta$$ between the applied force and the horizontal can be varied. The critical angle $$(\theta)$$ for which the spool does not roll and remains stationary is given by :
120425_9ffc1d8881384375adf1c4669b2c47e6.png
  • $$\theta=cos^{-1}\left (\cfrac {r}{R}\right )$$
  • $$\theta=cos^{-1}\left (\cfrac {2r}{R}\right )$$
  • $$\theta=cos^{-1}\sqrt {\cfrac {r}{R}}$$
  • $$\theta=sin^{-1}\left (\cfrac {r}{R}\right )$$
A body is in equilibrium under the influence of a number of forces. Each force has a different line of action. The minimum number of forces required is :
  • 2, if their lines of action pass through the centre of mass of the body.
  • 3, if their lines of action are not parallel.
  • 3, if their lines of action are parallel.
  • 4, if their lines of action are parallel and all the forces have the same magnitude.
A massless spool of inner radius r, outer radius R is placed against vertical wall and tilted split floor as shown. A light inextensible thread is tightly wound around the spool through which a mass m is hanging. There exists no friction at point A, while the coefficient of friction between spool and point B is $$\mu$$. The angle between two surfaces is $$\theta$$.

120066_c42ef264098e49578ac997b5db929736.png
  • the magnitude of force on the spool at B in order to maintain equilibrium is $$mg\sqrt {(\cfrac {r}{R})^2+(1-\cfrac {r}{R})^2\cfrac {1}{tan^2\theta}}$$
  • the magnitude of force on the spool at B in order to maintain equilibrium is $$mg \left (1-\cfrac {r}{R}\right )\cfrac {1}{tan\theta}$$
  • the maintain value of $$\mu$$ for the system to remain in equilibrium is $$\cfrac {cot\theta}{(R/r)-1}$$
  • the maintain value of $$\mu$$ for the system to remain in equilibrium is $$\cfrac {tan\theta}{(R/r)-1}$$
A small spherical ball is suspended through a string of length l. The whole arrangement is placed in a vehicle which is moving with velocity v. Now, suddenly the vehicle stops and ball starts moving along a circular path. If tension in the string at the highest point is twice the weight of the ball then (Assume that the ball completes the vertical circle)
  • $$\displaystyle v= \sqrt{5gl}$$
  • $$\displaystyle v= \sqrt{7gl}$$
  • velocity of the ball at highest point is $$\displaystyle \sqrt{gl}$$
  • velocity of the ball at the highest point is $$\displaystyle \sqrt{3gl}$$
A stone is tied to a string of length, $$\ell$$, and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed, $$u$$. The magnitude of the change in velocity as it reaches a position where the string is horizontal ($$g$$ being acceleration due to gravity) is
  • $$\sqrt{2g\ell}$$
  • $$\sqrt{2(u^2-g\ell)}$$
  • $$\sqrt{u^2-g\ell}$$
  • $$u-\sqrt{u^2-2g\ell}$$
A ball attached to one end of a string swings in a vertical plane such that its acceleration at point A (extreme position) is equal to its acceleration at point B (mean position). The angle $$\displaystyle \theta $$ is
241153_f9496279557d4904bb9091bca3f2336c.png
  • $$\displaystyle \cos ^{-1}\left ( \frac{2}{5} \right )$$
  • $$\displaystyle \cos ^{-1}\left ( \frac{4}{5} \right )$$
  • $$\displaystyle \cos ^{-1}\left ( \frac{3}{5} \right )$$
  • None of these
A ball tied to the end of the string swings in a vertical circle under the influence of gravity.
  • When the string makes an angle $$\displaystyle 90^{\circ}$$ with the vertical, the tangential acceleration is zero and radial acceleration is somewhere between minimum and maximum.
  • When the string makes an angle $$\displaystyle 90^{\circ}$$ with the vertical, the tangential acceleration is maximum and radial acceleration is somewhere between maximum and minimum.
  • At no place in circular motion, tangential acceleration is equal to radial acceleration.
  • When radial acceleration has its maximum value, the tangential acceleration is zero.
just before the sphere comes in contact with the peg.
241642_960f8fb22b3b47b08916aad356b6539f.png
  • $$\displaystyle \frac{mg}{2}$$
  • $$\displaystyle {mg}$$
  • $$\displaystyle \frac{3mg}{2}$$
  • $$\displaystyle \frac{5mg}{2}$$
if AB is a massless rod,
241618_a6dcbbca76ca462fa697f86d5b4ad63f.png
  • $$\displaystyle \frac{L}{2}$$
  • $$\displaystyle \frac{3L}{2}$$
  • $$\displaystyle \frac{5L}{2}$$
  • $$\displaystyle \frac{7L}{2}$$
A spool of mass $$M$$ and radius $$2R$$ lies on an inclined plane as shown in figure. A light thread is wound around the connecting tube of the spool and its free end carries a weight of mass $$m$$. The value of $$m$$ so that system is in equilibrium is

160455_0bc071fdbeee4eea9e4469502d62bc9d.png
  • $$2M\sin { \alpha } $$
  • $$M\sin { \alpha } $$
  • $$2M\tan { \alpha } $$
  • $$M\tan { \alpha } $$
A particle is given an initial speed $$u$$ inside a smooth spherical shell of radius $$R$$ so that it is just able to complete the circle. Acceleration of the particle, when its velocity is vertical, is
241234_a76d4e0330c84300b0f51247e3d0b554.png
  • $$\displaystyle g\sqrt{10}$$
  • $$\displaystyle  g$$
  • $$\displaystyle g\sqrt{2}$$
  • $$\displaystyle g\sqrt{6}$$
A simple pendulum is released from rest with the string in horizontal position. The vertical component of the velocity of the bob becomes maximum, when the string makes an angle $$\displaystyle \theta $$ with the vertical. The angle $$\displaystyle \theta $$ is equal to
  • $$\displaystyle \frac{\pi }{4}$$
  • $$\displaystyle \cos ^{-1}\left ( \frac{1}{\sqrt{3}} \right )$$
  • $$\displaystyle \sin ^{-1}\left ( \frac{1}{\sqrt{3}} \right )$$
  • $$\displaystyle \frac{\pi }{3}$$
A particle is moving in a circular path in the vertical plane. It is attached at one end of a string of length $$l$$ whose other end is fixed. The velocity at lowest point is $$u$$. The tension in the string is $$\displaystyle \vec{T}$$ and acceleration of the particle is $$\displaystyle \vec{a}$$ at any position. Then $$\displaystyle \vec{T}.\vec{a}$$ is zero at highest point if
  • $$\displaystyle u> \sqrt{5gl}$$
  • $$\displaystyle u= \sqrt{5gl}$$
  • Both (a) and (b) correct
  • Both (a) and (b) are wrong
A particle of mass $$m$$ is suspended by a string of length $$l$$ from a fixed rigid support. A sufficient horizontal velocity $$\displaystyle v_{0}= \sqrt{3gl}$$ is imparted to it suddenly. Calculate the angle made by the string with the vertical when the acceleration of the particle is inclined to the string by $$\displaystyle 45^{\circ}.$$
  • $$\displaystyle \theta = \frac{\pi }{2}$$
  • $$\displaystyle \theta = \frac{\pi }{3}$$
  • $$\displaystyle \theta = \frac{\pi }{4}$$
  • $$\displaystyle \theta = \pi $$
What is the maximum speed at which a railway carriage can move without toppling over along a curve of radius $$R=200m$$ if the distance from the centre of gravity of the carriage to the level of the rails is $$h=1.0m$$, the distance between the rails is $$h=1.0m$$, the distance between the rails is $$l=2.0m$$ and the rails are laid horizontally? (Take $$\displaystyle g= 10m/s^{2}$$)
  • $$\displaystyle 11.18ms^{-1}$$
  • $$\displaystyle 22.36ms^{-1}$$
  • $$\displaystyle 44.72ms^{-1}$$
  • $$\displaystyle 74ms^{-1}$$
just after it comes in contact with the peg.
241648_4ace1cfb86d1451eb9c94bb16a1b0f31.png
  • $$\displaystyle \frac{mg}{2}$$
  • $$\displaystyle mg$$
  • $$\displaystyle \frac{3mg}{2}$$
  • $$\displaystyle \frac{5mg}{2}$$
A car is travelling along a circular curve that has a radius of 50 m. If its speed is 16 m/s and is increasing uniformly at $$\displaystyle 8 m/s^{2},$$ determine the magnitude of its acceleration at this instant.
  • $$9.5\ m/s^2$$
  • $$9.8\ m/s^2$$
  • $$8.5\ m/s^2$$
  • $$7.5\ m/s^2$$
A thin circular wire of radius R rotates about its vertical diameter with an angular frequency $$\displaystyle \omega .$$ Show that a small bead on the wire remains at its lowermost point $$\displaystyle \omega \leq \sqrt{g\:l\:R}.$$ What is angle made by the radius vector joining the centre to the bead with the vertical downward direction for $$\displaystyle \omega = \sqrt{2g\:l\:R}?$$ Neglect friction.
  • $$\displaystyle 30^{\circ}$$
  • $$\displaystyle 45^{\circ}$$
  • $$\displaystyle 60^{\circ}$$
  • $$\displaystyle 90^{\circ}$$
The bob of the pendulum shown in figure describes an arc of circle in a vertical plane. If the tension in the cord is $$2.5\ times$$ the weight of the bob for the position shown. Find the velocity and the acceleration of the bob in that position.
242842_c97ec45661eb4d77ad78708ce148128f.png
  • $$\displaystyle 16.75ms^{-1}, 5.66ms^{-2}$$
  • $$\displaystyle 5.66ms^{-1}, 16.75ms^{-2}$$
  • $$\displaystyle 2.88ms^{-1}, 16.75ms^{-2}$$
  • $$\displaystyle 5.66ms^{-1}, 8.34ms^{-2}$$
The simple $$2 kg$$ pendulum is released from rest in the horizontal position. As it reaches the bottom position, the cord wraps around the smooth fixed pin at $$B$$ and continues in the smaller are in the vertical plane. Calculate the magnitude of the force $$R$$ supported by the pin at $$B$$ when the pendulum passes the position $$\displaystyle \theta = 30^{\circ}.\left ( g= 9.8m/s^{2} \right )$$
241754_c466f74d21ca402b97c3f122452090c2.png
  • $$15 N$$
  • $$30 N$$
  • $$45 N$$
  • $$60 N$$
A car is travelling along a circular curve that has a radius of $$50$$ m. If its speed is $$16$$ m/s and is incrcasing uniformly at $$\displaystyle 8m/s^{2}.$$ Determine the magnitude of its acceleration at this instant.
  • $$\displaystyle 7.5 ms^{-2}$$
  • $$\displaystyle 8.5 ms^{-2}$$
  • $$\displaystyle 9.5 ms^{-2}$$
  • $$\displaystyle 9.8 ms^{-2}$$
A uniform rod of length L is placed symmetrically on two walls as shown in the figure. The rod is in equilibrium. If $$N_1$$ and $$N_2$$ are the normal forces exerted by the walls on the rod then
295635_e32a8083ef164552bc8bd0f3e43024c2.png
  • $$N_1$$ < $$N_2$$
  • $$N_1$$ > $$N_2$$
  • $$N_1$$ = $$N_2$$
  • $$N_1$$ and $$N_2$$ would be in the vertical directions
The mass of the bob of a simple pendulum of length $$L$$ is $$m$$. If the bob is left from its horizontal position then the speedof the bob and the tension in the thread in the lowest position of the bob will be respectively:
281000.bmp
  • $$\;\sqrt{2gL}\;and\;3\;mg$$
  • $$\;3\;mg\;and \sqrt{2gL}$$
  • $$\;2\;mg\;and\;\sqrt{2gL}$$
  • $$\;2\;gL\;and\;3\;mg$$
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