CBSE Questions for Class 11 Engineering Physics Laws Of Motion Quiz 13 - MCQExams.com

A stone of mass 1 kg is tied to the end of a string of $$1m$$ length. It is whired in a vertical circel. If the velocity of the stone at the top be $$4m/s$$. What is the tension in the string (at that instant)?
  • $$6N$$
  • $$16N$$
  • $$5N$$
  • $$10N$$
A stone of mass $$1kg$$ is tied to one end of a string of length $$0.5\ m$$. It is whirled in a veretical circular. If the maximum tension in the string is $$58.8N$$, the velocity at the top is
  • $$1.82\ ms^{-1}$$
  • $$2.2\ ms^{-1}$$
  • $$3.26\ ms^{-1}$$
  • $$2.87\ ms^{-1}$$
A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 s, what is the magnitude & direction of acceleration of the stone: 
  • $$\pi^2 \ m/s^2$$ and direction along the tangent to the circle.
  • $$\pi^2 \ m/s^2$$ and direction along the radius towards the centre.
  • $$\frac{\pi^2}{4} \ m/s^2$$ and direction along the radius towards the centre.
  • $$\pi^2 \ m/s^2$$ and direction along the radius away from the centre.
Mass $$2m$$ is kept on a smooth circular track of mass $$m$$ , which is kept on a smooth horizontal surface. The circular track is given a horizontal velocity $$\sqrt{2gR}$$ towards left and released. The maximum height reached by $$2m$$ will be ?
1093626_e3768f1c273045dfb9e75433779b94b3.png
  • $$\dfrac {R}{4}$$
  • $$\dfrac {R}{2}$$
  • $$\dfrac {R}{3}$$
  • $$\dfrac {2R}{3}$$
A stone is tied to a rope is rotated in a vertical circle with unifrom speed. if the difference between maximum and minimum tension in the rope is $$20N$$, mass of the stone in $$Kg$$ is $$(g=10m/s^{2})$$
  • $$0.75$$
  • $$1.0$$
  • $$1.5$$
  • $$0.5$$
A ball of mass m strikes the fixed inclined plane inclined plane after falling through a height h. If it rebounds elastically, the impulse on the ball is:
1114328_219fadae37d44db8854c4f67060abf1f.png
  • $$2m\space cos\theta \sqrt(2gh)$$
  • $$2m\space cos\theta \sqrt(gh)$$
  • $$\dfrac{2m\sqrt(2gh)}{cos\theta} $$
  • $$2m \sqrt(2gh)$$
Two balls of the same mass are dropped from the same height h, on to the floor. The first ball bounces to a height $$h/4$$, after the collision & the second ball to a height $$h/16$$. The impulse applied by the first & second ball on the floor are $$I_1$$ and $$I_2$$ respectively. Then
  • $$5{I_1} = 6{I_2}$$
  • $$6{I_1} = 5{I_2}$$
  • $${I_1} = 2{I_2}$$
  • $$2{I_1} = {I_2}$$
Figure shows overhead views of three structure, on which three forcess act.The direction of the forces are as indivcated .If the magnitude of the forces are adjusted properly ,which structure can be in stable equilibrium

1116277_b6ba1dd222cb48ca802f57f20be211c6.png
  • A
  • B
  • C
  • Both (a) & (b)
A road is banked at an angle of $$30^{o}$$ to the horizontal for negotiating a circular road of radius $$10 m$$. At what velocity a car will experience no friction while negotiating the curve?
  • $$54\ km/hr$$
  • $$72\ km/hr$$
  • $$27.36\ km/hr$$
  • $$28\ km/hr$$
Select the incorrect option:-
($$\tau = torque, \,v = velocity, \,\omega = angular \,velocity, \, a_c = centripetal \, acceleration$$)
  • $$\vec \tau \times \vec \tau = 0$$
  • $$\vec v . \vec \omega = 0$$
  • $$ \vec \omega \times \vec v= 0$$
  • $$ \vec a_c \times \vec v= 0$$
A system of two blocks $$A$$ and $$B$$ are connected by an inextensible massless strings as shown. The pulley is massless and frictionless. Initially the system is at rest when, a bullet of mass $$m$$ moving with a velocity $$u$$ as shown hits the block $$B$$ and gets embedded into it.  The impulse imparted by tension force to the block of mass $$3m$$ is:
1123837_fd05fa19112c43cb877353fea75362ea.png
  • $$\cfrac{5mu}{4}$$
  • $$\cfrac{4mu}{5}$$
  • $$\cfrac{2mu}{5}$$
  • $$\cfrac{3mu}{5}$$
A ball of mass m is released from the top of an inclined plane of inclination $$\theta$$ as shown. It strikes a rigid surface at a distance $$\dfrac{3l}{4}$$ from top elasticity. Impulse imparted to ball by the rigid surface is:
1095605_3683198af19f4718be7bcc8c70851fe7.png
  • $$m\sqrt{\dfrac{3}{2}gh}$$
  • $$2m\sqrt {3gh}$$
  • $$m\sqrt {3gh}$$
  • $$m\sqrt {6gh}$$
A bob of mass $$m$$ is attached at one end of a string of length $$\iota $$. Other end of the string is fixed point $$O$$. Bob is rotating in circular path of radius $$\iota $$ in horizontal plane about $$O$$ with constant speed $$v$$, as shown in the figure. The average force exerted by string on the bob during its:
1113256_732aa066e6644d4ea2158224a5880d28.png
  • half revolution will be $$\dfrac{mv^{2}}{\pi \iota }$$
  • half revolution will be $$\dfrac{2mv^{2}}{\pi \iota }$$
  • one fourth revolution will be $$\dfrac{\sqrt{2mv^{2}}}{\pi \iota }$$
  • one revolution will be zero
The length of a ballistic pendulum is $$1\quad m$$ and mass of its block is $$0.98kg$$. A bullet of mass $$20$$ gram strikes the block along horizontal direction and gets embedded in the block. If block+bullet completes vertical circle of radius $$1m$$, then the striking velocity of bullet is
  • $$280m/s$$
  • $$350m/s$$
  • $$420m/s$$
  • $$490m/s$$
A pendulum of mass m=0.1 kg swing in a vertical plane at the end of a string of length, i=1m. if its speed v=2m/sec.when the string makes an angle $$\theta  = {30^0}$$  with the vertical, then tangential  acceleration.
  • 2 $$m/{s^{ - 1}}$$
  • 4 $$m/{s^{ - 2}}$$
  • 5 $$m/{s^{ - 1}}$$
  • 10 $$m/{s^{ - 1}}$$
Average force exerted by the ball on the ball is 
  • 5000 N
  • 2000 N
  • 2500 N
  • 6000 N
A $$10$$ gm bullet is fired from a rifle horizontally into a $$5$$ kg block of wood suspended by a string and the bullet gets embedded in the block. The impact causes the block to switch to an a height of $$2.5$$ cm above its initial level. The velocity of the bullet is
  • $$286.8 $$m/sec
  • $$350.7 $$m/sec
  • $$1000 $$m/sec
  • $$523 $$m/sec
The skate board negotiates the circular surface of radius 4.5 m. At $$\theta =45^0$$, its speed of centre of mass is 6 $$ms^{-1}$$. The combined mass of skate board and the person is 70 kg and his centre of mass is 0.75 m from the surface. The normal reaction between the surface and the skate board wheel is
1189606_576cd8ac24fe4dcba589b5443ed136f7.png
  • $$500 N$$
  • $$2040 N$$
  • $$1145 N$$
  • zero
If chains starts slipping find it kinetic energy when chain becomes complete straight :
1126601_5069fcf5c86f46e983a63f0c7e3310a5.png
  • $$mgl$$
  • $$2 \ mgl$$
  • $$\dfrac{4mgl}{9}$$
  • None of these
In the arrangement shown in figure, 5 kg block is placed on a rough table $$(\mu  = 0.4)$$ and a 3 kg mass is connected at one end, then the range of mass m, for which the system will remain in equilibrium is
1181846_4dabcb2db9fe44a4926407705a4cc3ce.png
  • $$1 kg$$ to $$3 kg$$
  • $$1 kg$$ to $$5 kg$$
  • Any value less than $$8 kg$$
  • $$3 kg$$ to $$5 kg$$
A car mass 1000 kg negotiates a banked curve of radius 90 m on a frictionless road. if the banking angle is $${ 45 }^{ o }$$, the speed of the car is :-
  • $$5\ m/s$$
  • $$10\ m/s$$
  • $$20\ m/s$$
  • $$30\ m/s$$
A car is moving on a straight road at a speed of 50 km/h and a truck is ahead of the car and having a large plane mirror fixed vertically on the back of truck. Truck is running at a speed of 70 km/h. For a stationary observer standing between car and truck. What is the speed of image of car in the mirror?
  • 40 km/h
  • 70 km/h
  • 20 km/h
  • 90 km/h
Four point charges are placed in a straight line with magnitude and separation as shown in the diagram. What should be the value of $${q_0}$$ such that $$ + 10\mu C\;ch\arg e$$ is in equlibrium?
1269899_572854433e4345c09be1b02ed4499b73.png
  • -80 $$\mu C$$
  • + 40 $$\mu C$$
  • +80 $$\mu C$$
  • -20 $$\mu C$$
Three point charges, each $$+q$$ are placed at the vertices of an equilateral triangle. What charge should be placed at its centroid so that all four charges are in equilibrium?
  • $$\cfrac{q} {\sqrt2}$$
  • $$\cfrac{q} {\sqrt3}$$
  • $$\cfrac{\sqrt3 q} {2}$$
  • $$\cfrac {2q} {\sqrt3}$$
A cubical bolck of wood of edge 10 cm and mass 0.92 kg floats on a tank of water with oil of relative density 0.6 to a depth of 4 cm above water.When the block attains equilibrium with four of its sides edges vertical:
  • 1 cm of it will be above the free surface of oil
  • 5 cm ofit will be under water
  • 2 cm of it will be above the common surface of oil and water.
  • 8 cm of it will be under water.
A mass is performing circular motion in a vertical plane centered at $$O$$. The average velocity of the particle is in creased, then at which point the string will break:
1275180_21aee9282cfd4d01ab3e89d98621f24b.PNG
  • $$A$$
  • $$B$$
  • $$C$$
  • $$D$$
Two free positive charges $$4q$$ and $$q$$ are a distance $$l$$ apart. What charges $$Q$$ is needed to achieve equilibrium for the entire system and where should it be placed from charge $$q$$ ?
  • $$Q=-\cfrac{4q}{9}$$ in between $$4q$$ and $$q$$ at $$\cfrac{l}{3}$$ from $$4q$$
  • $$Q=-\cfrac{4q}{9}$$ in between $$4q$$ and $$q$$ at $$\cfrac{2l}{3}$$ from $$4q$$
  • $$Q=\cfrac{4q}{9}$$ in between $$4q$$ and $$q$$ at $$\cfrac{l}{3}$$ from $$4q$$
  • $$Q=\cfrac{4q}{9}$$ in between $$4q$$ and $$q$$ at $$\cfrac{2l}{3}$$ from $$4q$$
Force applied on a body is given by $$ F = (3t^2 - 2t + 10) N$$ where t is in seconds. Find impulse in t = 0 to t = 2 sec.
  • $$ 24 Kg ms^{-1} $$
  • $$ 2.4 Kg ms^{-1} $$
  • $$ 24 Kg^{-1} ms^{-1} $$
  • $$ 2.4 Kg^{-1} ms^{-1} $$
A cyclist riding the bicycle at a speed of $$ \sqrt { 3 } m/s $$ takes a turn around a circular road of radius $$ 20 \sqrt { 3 } m $$ without skidding. What is his inclination to the vertical?
  • $$ 30 $$
  • $$ 40 $$
  • $$ 60 $$
  • $$ 75 $$
A long horizontal rod has a bead which can slide along its length and is initially placed at a distance $$L$$ from one end of the rod. The rod is set in angular motion about a vertical axis passing through A with a constant angular acceleration $$\alpha $$. The friction coefficient between the rod and the bead is $$\mu $$.Neglecting gravity, what is the time after which the bead starts slipping on the rod.
  • $$\sqrt {\frac{\mu }{\alpha }} $$
  • $$\frac{\mu }{{\sqrt \alpha }}$$
  • $$\sqrt {\frac{1}{{\mu \alpha }}} $$
  • $$\frac{1}{\mu }\sqrt {\frac{1}{\alpha }} $$
A mass of $$6\ kg$$ is suspended by a rope of length $$2\ m$$ from a ceiling. A force of $$50\ N$$ is applied in horizontal direction at the mid point of the rope. What is the angle between the rope and the vertical in equilibrium.
1293008_382c350dca9d49ce8aef62c4ae8bdca2.png
  • $$\tan^{-1} \left(\dfrac{4}{5} \right)$$
  • $$\tan^{-1} \left(\dfrac{5}{4} \right)$$
  • $$\tan^{-1} \left(\dfrac{5}{6} \right)$$
  • None
If the banking angle of curved road is given is given by $$\tan ^{ -1 }{ \left( \cfrac { 3 }{ 5 }  \right)  } $$ and the radius of curvature of the road is $$6m$$ then the sale driving speed should not exceed ($$g=10m/{s}^{2}$$)
  • $$86.4km/h$$
  • $$43.2km/h$$
  • $$21.6km/h$$
  • $$30.4km/h$$
For a paticle in a vertically circle with unifrom speed, the maximum and minimum tension in the string are in the ratio 5 : 3, if the radius of vertical circle is 2 m, the speed of revolving body is $$ ( g= 10 m/s^2) $$
  • $$ \sqrt {5} m/s $$
  • $$ 4 \sqrt {5} m/s $$
  • $$ 5 m/s $$
  • $$ 10 m/s $$
A point starts from rest and moves along a circular path with a constant tangential acceleration. After one rotation, the ratio of its radial acceleration to its tangential acceleration will be equal to:
  • $$1$$
  • $$2\pi$$
  • $$\cfrac{1}{2}\pi$$
  • $$4\pi$$
A uniform circular disc of radius R is placed on a smooth horizontal surface with its plane horizontal and hinged at circumference through point O as shown. An impulse P is applied at a perpendicular distance h from its centre C. The value of h so that the impulse due to hinge zero, is 
1298002_625f949dc7294a1f8143d3e3ed35661f.png
  • R
  • R/3
  • R/2
  • R/4
A road is banked at an angle of $$37^{ 0 }.$$ If a car moving at 54 km/hr does not experience any friction force while negotiating the curve, the radius of curve is :-
  • $$\dfrac { 67.5 }{ 4 } m$$
  • 45 m
  • 54 m
  • 30 m
A bullet of mass m strikes a pendulum bob of mass M with velocity u. It passes through and emerges out with a velocity u/2 from bob. The length of the pendulum is l. What should be the minimum value bob u if the pendulum bob will swing through a complete circle?
  • $$\frac{{2M}}{m}\times \,\sqrt {5gl\,} $$
  • $$\frac{M}{{2m}}\times \,\sqrt {5gl\,} $$
  • $$\frac{{2M}}{m}\times \,\dfrac{1}{{\sqrt {5gl\,} }}$$
  • $$\frac{M}{{2m}}\times \,\dfrac{1}{{\sqrt {5gl\,} }}$$
A partide is moving along a vertical circle of radius R.at P what will be the velocity of partide (assume critical condition at C)?
1298945_03280e5d0e2e4f1b9e1c6a13dd4afd9a.png
  • $$\sqrt {gR} $$
  • $$\sqrt {2gR} $$
  • $$\sqrt {3gR} $$
  • $$\sqrt {\frac{3}{2}gR} $$
A ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards right as shown. Relative to its initial position with respect to the table, the ball
I. Remains stationary if there is no friction between the paper and the ball.
II. Moves to the left and starts rolling backwards, i.e. to the left if there is a friction between the paper and the ball.
III. Moves forward, i.e., in the direction in which the paper is pulled.
Here, the correct statements is/ are
1277016_de22b0e4645541d6b8b6bf896980234d.png
  • I and II only
  • III only
  • I only
  • II only
A particle is whirled in a vertical circle of radius 1.0 m using a string with one end fixed. If the ratio of maximum and minimum tension in the string is $$\frac{5}{3}$$, the minimum velocity of the particle during circular motion is : 
1306298_69e73f61a12b472588a5bed446a5552f.GIF
  • $$\sqrt {10}$$ m/s
  • $$\sqrt {50}$$ m/s
  • $$10$$ m/s
  • $$10\sqrt 5$$ m/s
If four forces act at a point 'o' as shown in the figure and if O is in equilibrium then the value of '$$\theta $$' & 'p' are 
  • $${ 15 }^{ 0 },10\sqrt { 2N } $$
  • $${ 45 }^{ 0 }$$, 10 N
  • 40N
  • all the above
A simple pendulum has length l. The minimum velocity to be pendulum so that it performs vertical circular motion is
  • $$\sqrt {gl} $$
  • $$\sqrt2{gl} $$
  • $$\sqrt5{gl} $$
  • $$\sqrt {\frac{1}{g}} $$
A rod of mass $$5\ kg$$ is suspended with the help of two strings as shown in figure and remains in equilibrium. Linear mass density of rod is given by $$\mu = \lambda x^n$$ where $$x$$ is distance from left end of the rod. The value of $$n$$ is.
1324343_f122d0d2810e49a38f590a347915794f.PNG
  • $$3$$
  • $$2$$
  • $$5$$
  • $$4$$
A cube of size 10 cm is floating in equilibrium in a tank of water. When a mass of 10 gm is placed on the cube, the depth of cube inside water increase by $$(g=10m/{ s }^{ -2 }$$, density of water = $$1000kg/{ m }^{ 2 })$$
  • 0.1 mm
  • 4 m
  • 1 mm
  • 0.1 m
A circular coil radius 4 cm having 50 turns carries a current of 2A. it is placed in a uniform magnetic field of intensity 0.1 T. the work done to rotate the coil from the equilibrium position through $${ 180 }^{ \circ  }$$ is
  • $$\dfrac { 16\pi }{ 500 } J$$
  • $$\dfrac { 64\pi }{ 175 } J$$
  • $$\dfrac { 4\pi }{ 125 } J$$
  • $$\dfrac { 2\pi }{ 25 } J$$
Consider a pendulum bob of length $$\ell$$ hanging on a thin rod. Rod is given just sufficient velocity such that it negotiates vertical circle.
Statement-1: Minimum velocity at top most point of circle is nearly zero.
Statement-2: In order to complete circle tension in rod is always nonzero during motion from lowest to topmost point.
  • Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
  • Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
  • Statement-1 is true, statement-2 is false.
  • Statement-1 is false, statement-2 is true.
Two bodies $$A$$ and $$B$$ of masses $$20kg$$ and $$5kg$$ respectively. Each one is acted upon by a force of $$4kg$$ $$wt.$$. If they acquire the same kinetic energy in times $${t}_{A}$$ and $${t}_{B}$$, then ratio of $$\cfrac{{t}_{A}}{{t}_{B}}$$ is:
  • $$\cfrac{1}{2}$$
  • $$\cfrac{2}{5}$$
  • $$\cfrac{5}{6}$$
  • $$2$$
A wire of density $$\rho  $$and cross-sectional area A forms three side of a square and is free to rotate the horizontal axis $${ OO }^{ 1 }.$$ A magnetic field B exists in the vertically upward direction. When a current k is passed through the wire, the system comes to equilibrium at angle $$\theta $$ to the vertical.Then the value of $$\theta $$ is given by.
  • $$cos\theta =\dfrac { 2A\rho g }{ iB } $$
  • $$cot\theta =\dfrac { 2A\rho g }{ iB } $$
  • $$tan\theta =\dfrac { A\rho g }{ 2iB } $$
  • $$sin\theta =\dfrac { A\rho g }{ 2iB } $$
A write of density $$p$$ and cross-sectional area A forms three sides if a square and is free to rotate about the horizontal axis $${ OO }^{ 1 }$$. A magnetic field B exist in the vertically upward direction. When a current  i is   passed through the wire, the system come to equilibrium at angle $$\theta $$ to the vertical. Then the value if $$\theta $$ is given by
1324805_584bb3940b6f4c01b72331abb651db96.JPG
  • $$\cos { \theta } =\dfrac { 2Apg }{ iB } $$
  • $$\cot { \theta } =\dfrac { 2Apg }{ iB } $$
  • $$\tan { \theta } =\dfrac { Apg }{ 2iB } $$
  • $$\sin { \theta } =\dfrac { Apg }{ 2iB } $$
In a carom-board game the striker and the coins are identical and of mass m. In a particular hit the coin is hit when it is placed close to the edge of the board as shown in figure such that the coin travels parallel to the edge. If the striker is moving with speed v before the strike , then the net impulse on the striker during collision if it moves perpendicular to the edge is (assume all collisions to be perfectly elastic)
1319096_0b375b268d45492eba2d60506870c4fc.png
  • $$mv\sqrt { \dfrac { 5 }{ 2 } } $$
  • $$2 mv $$
  • $$ \dfrac { mv\sqrt { 3 } }{ 2 } $$
  • mv
0:0:1


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