CBSE Questions for Class 11 Engineering Physics Laws Of Motion Quiz 4 - MCQExams.com

A pendulum hangs from the ceiling of a jeep moving with a speed, $$v$$, along a circle of radius, $$R$$. Find the angle with the vertical made by the pendulum.
  • $$0$$
  • $$\tan ^{-1}\displaystyle \frac{v^{2}}{Rg}$$
  • $$\tan ^{-1}\displaystyle \frac{Rg}{v^{2}}$$
  • None of the above
A simple pendulum has a bob of mass m and swings with an angular amplitude $$\phi$$. The tension in the thread is T. At a certain time, the string makes an angle $$\theta$$ with the vertical ($$\theta \le \phi$$)
  • $$T = mg \cos \theta$$, for all values of $$\theta$$
  • $$T = mg \cos \theta$$, only for $$\theta = \phi$$
  • $$T = mg$$, for $$\displaystyle \theta =\cos^{-1} \left[\frac{1}{3}(2cos\phi +1)\right]$$
  • T will be larger for smaller values of $$\theta$$
 A simple pendulum is oscillating without damping. When the displacement of the bob is less than maximum, its acceleration vector $$\overrightarrow{a}$$ is correctly shown in
A stone tied to a string of length $$L$$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time the stone is at its lowest position and has a speed $$u$$.The magnitude of change in its velocity as it reaches a position, where the string is horizontal is
  • $$\sqrt{u^2 - 2gL}$$
  • $$\sqrt{2gL}$$
  • $$\sqrt{u^2 - gL}$$
  • $$\sqrt{2(u^2 - gL)}$$
A circular track of radius $$100$$ m is designed for an average speed $$54$$ km/h. Find the angle of banking.
  • $$ \tan ^{ -1 }{ \left( \dfrac { 3 }{ 20 } \right) } $$
  • $$ \tan ^{ -1 }{ \left( \dfrac { 9 }{ 40 } \right) } $$
  • $$ \tan ^{ -1 }{ \left( \dfrac { 3 }{ 10 } \right) } $$
  • None of these
A simple pendulum has a string of length $$l$$ and bob of mass $$m$$. When the bob is at its lower position, it is given the maximum horizontal speed necessary for it to move in a circular path about the point of suspension. The tension in the string at the lowest position of the bob is
  • $$ mg$$
  • $$3 mg$$
  • $$\sqrt {10} mg$$
  • $$4 mg$$
A particle moves along a vertical circle of radius r with a velocity $$ \sqrt { 8rg } $$ at Y. $$ { T }_{ A }$$, $$ { T }_{ B } $$, $$ { T }_{ x }$$, $$ { T }_{ y } $$ respresent tension at A, B, X and Y, respectively, then

135244.jpg
  • $$ { T }_{ A } = { T }_{ B } $$
  • $$ { T }_{ X } - { T }_{ Y } =6mg$$
  • $$ { T }_{ Y } - { T }_{ X } =6mg$$
  • $$ { T }_{ Y } > { T }_{ X } \neq 6mg$$
A particle of mass, $$m$$, is tied to a light string and rotated with a speed, $$v$$, along a circular path of radius, $$r$$. If $$T=$$ tension in the string and $$mg =$$ gravitational force on the particle, then the actual forces acting on the particle are
  • $$mg$$ and $$T$$ only.
  • $$mg$$, $$T$$ and an additional force of $$mv^2/r$$ directed inwards.
  • $$mg$$, $$T$$ and an additional force of $$mv^2/r$$ directed outwards.
  • Only a force $$mv^2/r$$ directed outwards.
Which of the following must be true for the sum of the magnitude of the momenta of the individual particles in the system?
  • It must be zero
  • It could be non-zero, but it must be a constant
  • It could be non zero, and it might not be a constant
  • It could be zero, even if the magnitude of the total momentum is not zero
Let $$\theta$$ denote the angular displacement of a simple pendulum oscillating in a vertical plane. If the mass of the bob is m, then tension in the string is mg $$\cos\theta$$
  • always
  • never
  • at the extreme position
  • at the mean position
Water in a bucket is whirled in a vertical circle with a string to it. The water does not fallen even when the bucket is inverted at the top of its path . We conclude that in this position:
  • $$\displaystyle mg = \frac{mv^2}{r}$$
  • $$mg$$ is greater than $$\displaystyle \frac{mv^2}{r}$$
  • $$mg$$ is not greater than $$\displaystyle \frac{mv^2}{r}$$
  • $$mg$$ is not less than $$\displaystyle \frac{mv^2}{r}$$
A balloon has $$5g$$ of air. A small hole is pierced into it. The air escapes at a uniform rate with a velocity of $$4cm/s$$. If the balloon shrinks completely in $$2.5$$ seconds, then the mean force acting on the balloon is:
  • $$2dyne$$
  • $$50dyne$$
  • $$8dyne$$
  • $$8N$$
The magnitude of force (in $$N$$) acting on a body varies with time $$t$$ (in $$\mu s)$$ as shown. $$AB, BC$$ and $$CD$$ are straight line segments. The magnitude of total impulse of force on the body from $$t=4\mu s$$ to $$t=16\mu s$$ is :

136794.PNG
  • $$ { 10 }^{ -3 }Ns$$
  • $$ { 10 }^{ -2 }Ns$$
  • $$ { 10 }^{ -4 }Ns$$
  • $$5\times { 10 }^{ -4 }Ns$$
A particle P of mass m attached to a vertical axis by two strings AP and BP of length 1m each. The separation $$AB = l$$. P rotates around the axis with an angular velocity $$\omega$$. The tension in the two strings are $$T_1$$ and $$T_2$$.

135966_e9ed1498da4c48e98231b86d49543225.png
  • $$T_1 = T_2$$
  • $$T_1 + T_2 = m\omega^2l$$
  • $$T_1 - T_2 = 2mg$$
  • BP will remain taut only if $$\omega \ge \sqrt{2g/l}$$
A stone tied to string of length $$l$$ is whirled in a vertical circle with the other end of the string at 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 is
  • $$\sqrt{u^2-2gl}$$
  • $$\sqrt{2gl}$$
  • $$\sqrt{u^2-gl}$$
  • $$\sqrt{2(u^2-gl)}$$
A bead $$A$$ can slide freely along a smooth rod bent in the form of a half circle of Radius $$R$$. The system is set in rotation with a constant angular velocity $$\omega$$ about a vertical axis $$OO'$$. Find the angle $$\theta$$ corresponding to steady position of the bead.

136077_b4d599dfd537428787e17c685f28bbeb.png
  • $$\cos ^{ -1 }{ \left( \cfrac { R{ \omega }^{ 2 } }{ g } \right) } $$
  • $$\cos ^{ -1 }{ \left( \cfrac { g }{ R{ \omega }^{ 2 } } \right) } $$
  • $$\sin ^{ -1 }{ \left( \cfrac { g }{ R{ \omega }^{ 2 } } \right) } $$
  • $$\sin ^{ -1 }{ \left( \cfrac { R{ \omega }^{ 2 } }{ g } \right) } $$
A simple pendulum rotates in a horizontal plane with an angular velocity $$\omega$$ about a fixed point P in a gravity free space. There is a negative charge at P. The bob gradually emits photo electrons(Leave the energy and momentum of incident photons and emitted electrons). The total force acting on the bob is $$T$$ .
  • $$T$$ will decrease, $$\omega$$ will decrease
  • $$T$$ will decrease, $$\omega$$ will remain constant
  • $$T$$ and $$\omega$$ will remain unchanged
  • The elastic strain in the string will decrease
A stone of mass $$1000g$$ tied to a light string of length $$10/3m$$ is whirling in a vertical circle. If the ratio of the maximum tension to minimum tension is $$4$$ and $$g=10{ ms }^{ -2 }$$, then the speed of stone at the highest point of circle is :
  • $$20{ ms }^{ -1 }$$
  • $$10\sqrt { 3 } { ms }^{ -1 }$$
  • $$5\sqrt { 3 } { ms }^{ -1 }$$
  • $$10{ ms }^{ -1 }$$
A stone of mass $$1\ kg$$ tied to a light inextensible string of length. $$L = \dfrac{10}{3}$$ metre is whirling in a circular path of radius, $$L$$, in a vertical plane. If the ratio of maximum tension to the minimum tension is $$4$$ and if $$g$$ is taken to be $$10\ m/s^{2}$$, the speed of the stone at the highest point of circle is :
  • $$20\ m/s$$
  • $$10 \sqrt{3}\ m/s$$
  • $$10\ m/s$$
  • $$5\sqrt{2}\ m/s$$
A toy car is tied to the end of an unstretched string of a length, $$a$$. When revolved, the toy car moves in a horizontal circle of radius $$2a$$ with time period, $$T$$. If it is now revolved in a horizontal circle of radius $$3a$$ with a period $$T'$$ with the same force, then
  • $$\displaystyle T' = \dfrac{\sqrt{3}}{2} T$$
  • $$\displaystyle T' = \sqrt {\dfrac{3}{2}} T$$
  • $$T' = T$$
  • $$\displaystyle T' = \dfrac{3}{2} T$$
A body of mass $$1\ kg$$ is rotating in a vertical circle of radius $$1\ m$$. What will be the difference in its kinetic energy at the top and bottom of the circle? 
Take $$g = 10\ m/s^{2}$$
  • $$50\ J$$
  • $$30\ J$$
  • $$20\ J$$
  • $$10\ J$$
The velocity of a particle at highest point of the vertical circle is $$\sqrt{3rg}$$. The tension at the lowest point, if mass of the particle is $$m$$, is
  • $$2\ mg$$
  • $$4\ mg$$
  • $$6\ mg$$
  • $$8\ mg$$
A truck has a width of $$2.8\ m$$. It is moving on a circular road of radius $$48.6\ m$$. The height of centre of mass is $$1.2\ m$$. The maximum speed so that it does not over turn will be nearly
  • $$24.3\ m/s$$
  • $$27.2\ m/s$$
  • $$13.4\ m/s$$
  • $$15.7\  m/s$$
At a curved path of the road, the road bed is raised a little on the side away from the centre of the curved path. The slope of the road bed is given by
  • $$\tan{\theta} = rg/v^2$$
  • $$\tan{\theta} = r/gv^2$$
  • $$\tan{\theta} = v^2/rg$$
  • $$\tan{\theta} = v^2g/r$$
A stone of mass $$1\ kg$$ is tied of the end of a string $$1\ m$$ long. It is whirled in a vertical circle. If the velocity of stone at the top is $$4\ m/s$$. What is the tension in the string at the lowest point? 
Take $$g = 10\ m/s^{2}$$
  • $$6\ N$$
  • $$66\ N$$
  • $$5.2\ N$$
  • $$76\ N$$
For traffic moving at $$60 km/hr$$ along a smooth circular track of radius $$0.1 km$$, the correct angle of banking should be:
  • $$\displaystyle tan^{-1} \left [ \frac{(100 \times 9.8)}{\left ( \frac{50}{3} \right )^2} \right ]$$
  • $$\displaystyle tan^{-1} \left [ \frac{\left ( \frac{50}{3} \right )^2}{(100 \times 9.8)} \right ]$$
  • $$tan^{-1} \displaystyle \left ( \frac{60^2}{0.1} \right )$$
  • $$tan^{-1} \sqrt{(60 \times 0.1 \times 9.8)}$$
If a particle of mass m moving with velocity $$v_1$$ is subject to an impulse $$I$$ which produces a final velocity $$v_2$$, then $$I$$ is given by :
  • $$m(v_1 - v_2)$$
  • $$m(v_1 + v_2)$$
  • $$m(v_2 - v_1)$$
  • $$\dfrac{m\left(v_2^2 - v_1^2\right)}{2}$$
A small sphere is attached to a cord and rotates in a vertical circle about a point $$O$$. If the average speed of the sphere is increased, the cord is most likely to break at the orientation when the mass is at
201363.png
  • Bottom point $$B$$
  • Top point $$A$$
  • Point $$D$$
  • Point $$C$$
A cricket ball of mass 500 gm strikes a bat normally with a velocity 30 m/s and rebounds with a velocity 20 m/s in the opposite direction. The impulse of the force exerted by the ball on the bat is:
  • 0.5 N.s
  • 1.0 N.s
  • 25 N.s
  • 50 N.s
A body $$X$$ of mass $$5 kg$$ is moving with velocity $$20 m s^{-1}$$ while another body Y of mass $$20 kg$$ is moving with velocity $$5 m s^{-1}$$. Compare the momentum of the two bodies.
  • $$1 : 4$$
  • $$4 : 1$$
  • $$1 : 2$$
  • $$1 : 1$$
Find the maximum speed at which a truck can safely travel without toppling over, on a curve of radius $$250m$$. The height of the centre of gravity of the truck above the ground is $$1.5 m$$ and the distance between the wheels is $$1.5m$$, the truck being horizontal.
  • $$\displaystyle 15\:ms^{-1}$$
  • $$\displaystyle 25\:ms^{-1}$$
  • $$\displaystyle 30\:ms^{-1}$$
  • $$\displaystyle 35\:ms^{-1}$$
A car of mass $$600 kg$$ is moving with a speed of $$10 m s^{-1}$$ while a scooter of mass $$80 kg$$ is moving with a speed of $$50 m s^{-1}$$. Compare their momentum.
  • $$2 : 3$$
  • $$1 : 2$$
  • $$3 : 1$$
  • $$3 : 2$$
A simple pendulum is vibrating with angular amplitude of $$\theta=90^{o}$$ as shown in figure.
For what value of $$\theta$$ is the acceleration directed
$$(i)$$ Vertically upwards
$$(ii)$$ Horizontally
$$(iii)$$ Vertically downwards
204018.png
  • $$0^{o},90^{o} \ cos^{-1}\displaystyle\frac{1}{\sqrt {3}},\ 90^{o}$$
  • $$ \cos^{-1}\displaystyle\frac{1}{\sqrt {3}},\ ,\ 0^{o},90^{o}$$
  • $$0^{o},90^{o}, \cos^{-1}\displaystyle\frac{1}{\sqrt{2}},$$
  • $$ \cos^{-1}\displaystyle\frac{1}{\sqrt {3}},\ 90^{o},\ 0^{o}$$
A pendulum bob is raised to a height, $$h$$, and released from rest. At what height will it attain half of its maximum speed?
  • $$\displaystyle\frac{3h}{4}$$
  • $$\displaystyle\frac{h}{2}$$
  • $$\displaystyle\frac{h}{4}$$
  • $$0.707h$$
A simple pendulum of length $$l$$ has maximum angular displacement $$\displaystyle \theta .$$ Then maximum kinetic energy of a bob of mass $$m$$ is
  • $$\displaystyle \frac{1}{2}mgl$$
  • $$\displaystyle \frac{1}{2}mgl\cos \theta $$
  • $$\displaystyle mgl\left ( 1-\cos \theta \right )$$
  • $$\displaystyle \frac{1}{2}mgl\sin \theta $$
The kinetic energy of particle at the lower most position is
241354_2b115582dc844347af732b651144fdb4.png
  • $$\displaystyle \frac{4mgL}{3}$$
  • $$2mgL$$
  • $$\displaystyle \frac{8mgL}{3}$$
  • $$\displaystyle \frac{2mgL}{3}$$
With what minimum speed $$v$$ must a small ball should be pushed inside a smooth vertical tube from a height $$h$$ so that it may reach the top of the tube? Radius of the tube is $$R$$.

237408_13c1a8f91301433d89a9add80a5365ef.png
  • $$\displaystyle \sqrt{g(R-h)}$$
  • $$\displaystyle \sqrt{g(2R-h)}$$
  • $$\displaystyle \sqrt{2g(2R-h)}$$
  • $$\displaystyle \sqrt{2g}$$
A bob is suspended from a crane by a cable of length $$5m$$. The crane and load are moving at a constant speed $$v_{0}$$. The crane is stopped by a bumper and the bob on the cable swings out an angle of $$60^{\circ}$$. Find the initial speed $$v_{0}.(g=9.8 m/s^{2})$$

237417_b16cb54503674fdfb9d1873f2863fa46.png
  • $$2 ms^{-1}$$
  • $$3 ms^{-1}$$
  • $$5 ms^{-1}$$
  • $$7 ms^{-1}$$
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 $$8 m/s$$ $$^{2}$$. Determine the magnitude of its acceleration at this instant.
  • 5.5 m/s$$^{2}$$
  • 7.5 m/s$$^{2}$$
  • 9.5 m/s$$^{2}$$
  • 12.5 m/s$$^{2}$$
A stone tied to a string of length $$L$$ is swired in a verticle circle with the other end of the string at the centre. At a certain instant of time the stone is at it lowest position and has a speed $$u$$. Find the magnitude of the change in its velocity as it reaches a position, where the string is horizontal.
  • $$\displaystyle \sqrt{(u^{2}-gL)}$$
  • $$\displaystyle \sqrt{2(u^{2}-gL)}$$
  • $$\displaystyle \sqrt{(u^{2}-2gL)}$$
  • $$\displaystyle \sqrt{2(u^{2}-2gL)}$$
Velocity of particle when it is moving vertically downward is
241362_370ea76a3e3f42fa807e92b218e45378.png
  • $$\displaystyle \sqrt{\frac{10gL}{3}}$$
  • $$\displaystyle 2\sqrt{\frac{gL}{3}}$$
  • $$\displaystyle \sqrt{\frac{8gL}{3}}$$
  • $$\displaystyle \sqrt{\frac{13gL}{3}}$$
Minimum velocity of the particle is
241345_791d0bb19e1f415c963bd4ae2ef0321e.png
  • $$\displaystyle 4\sqrt{\frac{gL}{3}}$$
  • $$\displaystyle 2\sqrt{\frac{gL}{3}}$$
  • $$\displaystyle \sqrt{\frac{gL}{3}}$$
  • $$\displaystyle 3\sqrt{\frac{gL}{3}}$$
if AB is a massless string.
241625_42f8088de9424f6480aa092d61eae401.png
  • $$\displaystyle \frac{10L}{27}$$
  • $$\displaystyle \frac{20L}{27}$$
  • $$\displaystyle \frac{30L}{27}$$
  • $$\displaystyle \frac{40L}{27}$$
A mass is performing vertical circular motion (see figure). If the average velocity of the particle is increased, then at which point is the maximum breaking possibility of the string:
280422.bmp
  • A
  • B
  • C
  • D
An instrument box placed on a table is given a push. It is observed that it stops its motion after some time. What is the force that stopped its motion?
  • Gravitational force
  • Tension force
  • Friction force
  • Mechanical force
A car moves on a circular road, describing equal angles about the centre in equal intervals of times which of the statements about the velocity of car
  • velocity is constant
  • magnitude of velocity is constant but the direction of velocity change
  • both magnitude and velocity change
  • velocity is directed towards the centre of circle
A boy is whirling a stone tied at one end such that the stone is in uniform circular motion.Which of the following statement is correct?
245814_7d3f89bb93574ce29b4797732a70bd81.png
  • The velocity of stone at A is equal to the velocity of stone B
  • The speed of stone at A is equal to the speed of stone at B.
  • The centripetal force is radially outward in the string.
  • All of the above statements are correct.
A force of $$50 \ dynes$$ is acted on a body of mass $$5 g$$ which is at rest for an interval of $$3 s$$, then impulse  is:
  • $$0.15\times 10^{-13}Ns$$
  • $$0.98\times 10^{-3}Ns$$
  • $$1.5\times 10^{-3}Ns$$
  • $$2.5\times 10^{-3}Ns$$
A turn has a radius of $$10 m$$. If a vehicle goes round it at an average speed of $$18$$ km/h, what should be the proper angle of banking?
  • $$\displaystyle \tan ^{-1}\left ( 1/4 \right )$$
  • $$\displaystyle \tan ^{-1}\left ( 1/2 \right )$$
  • $$\displaystyle \tan ^{-1}\left ( 3/4 \right )$$
  • $$\displaystyle \tan ^{-1}\left ( 5/7 \right )$$
A boy holds a pendulum in his hand while standing at the edge of a circular platform of radius $$r$$ rotating at an angular speed $$\omega$$. The pendulum will hang at an angle $$\theta$$ with the verticle such that
  • $$\;tan\,\theta=0$$
  • $$\;tan\,\theta=\displaystyle\frac{\omega^2r^2}{g}$$
  • $$\;tan\,\theta=\displaystyle\frac{r\omega^2}{g}$$
  • $$\;tan\,\theta=\displaystyle\frac{g}{\omega^2r}$$
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