Untitled Document

Question Bank No: 1

1. There is change of angular momentum from $\int$ to 4J in 4s,then the torque is

a)		3J/4
b)		1J
c)		5/4J
d)		4/3J

2. A ring and a disc of different masses are rotating with the same kinetic energy. If we apply a retarding torque $τ$ on the ring, it slops after making n revolutions.After how many revolutions will the disc stop if the retarding torque on it is also $τ ?$

a)		n/2
b)		n
c)		2n
d)		4n

3. When a body starts to roll on an inclined plane its potential energy is converted into

a)		translational KE only
b)		translational and rotational KE
c)		rotational KE only
d)		None of these

4. A solid sphere rolls down an inclined plane and its velocity at the bottom is $v_{1} .$ The same sphere slides down the plane (without friction) and its velocity at the bottom is $v_{2} .$ Which of the following relations is correct?

a)		$v_{1} = v_{2}$
b)		$v_{1} = \sqrt{\frac{5}{7}} v_{2}$
c)		$v_{1} = \sqrt{\frac{7}{5}} v_{2}$
d)		None of these

5. The moment of inertia of a solid cylinder about its axis is 1.It is allowed to roll down an inclined plane without slipping.If its angular velocity at the bottom be w,then kinetic energy of the cylinder will be

a)		$\frac{1}{2} {1 w}^{2}$
b)		${1 w}^{2}$
c)		${\frac{3}{2} lw}^{2}$
d)		21 $w^{2}$

6. Two wheels are mounted side by side and each is marked with a dot on its rim.The two dots are aligned with the wheels at rest,then one wheel is given a constant angular acceleration of $\frac{π}{2} rad / . \sec^{2}$ and the other $\frac{π}{4} rad / \sec^{2}$ .Then the two dots become alligned again for the first time after

a)		2s
b)		4s
c)		1s
d)		8s

7. A uniform metre stick of mass M is hinged at one end and supported in a horizontal direction by a string attached to the other end.What should be the initial acceleration of the stick,if string is cut?

a)		$\frac{3}{2} g rad / s^{2}$
b)		$g rad / s^{2}$
c)		3 $g rad / s^{2}$
d)		$4 g rad / s^{2}$

8. A particle of mass m moves with a constant velocity.Which of the following statements is not correct about its angular momentum about point 0?
centreofmass-Q18

a)		It is zero when it is at A and moving along 0A
b)		It is same at all points along the line DE
c)		It is of the same magnitude but oppositely directed at B and D
d)		It increases as it moves along the line BC

9. A flywheel of radius 2 m and mass 8kg rotates at an angular speed of 4 rad/s about an axis perpendicular to it through its centre.The kinetic energy of rotation is

a)		128 J
b)		196 J
c)		256 J
d)		392 J

10. A string is wrapped around a cylinder of mass M and radius R.The string is pulled vertically upwards to prevent the centre of mass from falling as the cylinder unwinds the string.The tension in the string is

a)		Mg/6
b)		Mg/3
c)		Mg/2
d)		Mg/3

11. A thin hollow cylinder is free to rotate about its geometrical axis .It has a mass of 8kg and a radius of 20 cm. A rope is wrapped around the cylinder.What force must be exerted along the rope to produce an angular arc of 3 rad/ $s^{- 1} ?$

a)		8.4N
b)		5.8N
c)		4.8N
d)		None of these

12. A ring is rolling on a surface without slipping .What is the ratio of its translational to rotational kinetic energies?

a)		5:7
b)		2:5
c)		2:7
d)		1:1

13. A uniform sphere of mass 200 gm rolls will be slipping on a plane surface so that its centre moves at a speed of 2.00 cm/s.Its KE is

a)		5.6 $\times 10^{- 5} J$
b)		5.6 $\times 10^{- 4} J$
c)		5.6 $\times 10^{- 3} J$
d)		5.6 $\times 10^{- 2} J$

14. A wheel initially at rest,is rotated with a uniform angular acceleration.The wheel rotates through an angle $θ_{1}$ in the first one second and through an additional angle $θ_{2}$ in the next one second.The ratio $\frac{θ_{2}}{θ_{1}}$ is

a)		4
b)		3
c)		2
d)		1

15. An electric fan has blades of length 30 cm as measured from the axis of rotation.If the fan is rotating at 1,200 rpm,the acceleration of a point on the tip of a blade is about

a)		4740 m/ $s^{2}$
b)		5055 m/ $s^{2}$
c)		1600 m/ $s^{2}$
d)		2370 m/ $s^{2}$

16. A uniform disc of mass M and radius R is mounted on an axle supported in frictionless bearings.A light cord is wrapped around the rim of the disc and a steady downward pull T is exerted on the cord.The angular acceleration of the disc is

a)		$\frac{T}{MR}$
b)		$\frac{MR}{T}$
c)		$\frac{2 T}{MR}$
d)		$\frac{MR}{2 T}$

17. Two circular discs are of same thickness.The diameter of A is twice that of B.The moment of inertia of A as compared to that of B is

a)		twice as large
b)		four times as large
c)		8 times as large
d)		16 times as large

18. Three point masses m are placed at the vertices of an equilateral triangle of side a.Moment of inertia of the system about an axis COD passing through a mass m at O and lying in the plane of AOB and perpendicular to OA is
centreofmass-Q8

a)		${2 ma}^{2}$
b)		${\frac{2}{3} ma}^{2}$
c)		${\frac{5}{4} ma}^{2}$
d)		${\frac{7}{4} ma}^{2}$

19. If the radius of a solid sphere is 35cm,calculate the radius of gyration when the axis is along a tangent

a)		7 $\sqrt{10} cm$
b)		7 $\sqrt{35} cm$
c)		7 $/ 5 cm$
d)		2 $/ 5 cm$

20. A ring,a solid sphere and disc have the same mass and radius.Which of them have the largest moment of inertia?

a)		Ring
b)		Solid Sphere
c)		Disc
d)		All have the same moment of inertia

21. A block Q of mass M is placed on a horizontal frictionless surface AB and a body P of mass m is released on its frictionless slope.As P slides by a length L on this slope of inclination $θ,$ the block Q would slide by a distance
centreofmass-Q5

a)		$\frac{m}{M} Lcos θ$
b)		$\frac{m}{M + m} L$
c)		$\frac{M + m}{m Lcos θ}$
d)		$\frac{m Lcos θ}{M + m}$

22. Two blocks of masses 5kg and 2kg are placed on a frictionless surface and connected by a spring.An external kick gives a velocity of 14 m/s to the heavier block in the direction of lighter one.The velocity gained by centre of mass is

a)		14 m/s
b)		7 m/s
c)		12 m/s
d)		10 m/s

23. The centre of mass of a system of particle does not depend on

a)		masses of the particles
b)		forces on the particles
c)		position of the particles
d)		relative distance between the particles

24. A circular plate of uniform thickness has a diameter of 56cm.A circular portion of diameter 42 cm is removed from one edge as shown in the figure.The centre of mass of the remaining portion from the centre of plate will be

a)		5cm
b)		7cm
c)		9cm
d)		11cm

25. Three particles of masses 1 kg,2 kg and 3kg are situated at the corners of an equilateral triangles of side b.The coordinates of the centre of mass are

a)		$[0, \frac{7 b}{12}, \frac{3 \sqrt{3} b}{12}]$
b)		$[3 \frac{\sqrt{3} b}{12}, \frac{7}{12} b, 0]$
c)		$[\frac{7 b}{2}, \frac{3 \sqrt{3} b}{12}, 0]$
d)		$[\frac{7 b}{12} . b, \frac{3 \sqrt{3} b}{12}]$

26. $S_{1}$ and $S_{2}$ are two spheres of equal masses. $S_{1}$ rolls down a smooth inclined plane of length 5 cm and height 4 cm. $S_{2}$ falls vertically down by 4 cm. The work done by $S_{1}$

a)		is greater than the work done by $S_{2}$
b)		and that by $S_{2}$ are same and non zero
c)		is less than the work done by $S_{2}$
d)		as well as $S_{2}$ is zero

27. When sand is poured on a rotating disc, its angular velocity will

a)		decrease
b)		increase
c)		remains constant
d)		none of these

28. A thick-walled hollow sphere has outer radius R. It rolls down an inclined plane without slipping and its speed at the bottom is v. If the inclined plane is frinctionless and the sphere slides down without rolling, its speed at the bottom will be 5v/4. What is the radius of gyration of the sphere?

a)		$\frac{R}{\sqrt{2}}$
b)		$\frac{R}{2}$
c)		$\frac{3 R}{4}$
d)		$\frac{\sqrt{3} R}{4}$

29. Two bodies with moment of inertia $I_{1}$ and $I_{2} (I_{1} > I_{2}),$ have equal angular momenta. If $E_{1}$ and $E_{2}$ be their KE of rotation, then

a)		$E_{1}$ = $E_{2}$
b)		$E_{1}$ > $E_{2}$
c)		$E_{1}$ < $E_{2}$
d)		$E_{1}$ $\geq$ $E_{2}$

30. Let g be acceleration due to gravity on the surface of the earth and $K_{r}$ be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2% keeping all other quantitites same (even w) :

a)		g decrease by 2% and $K_{R}$ decreases by 4%
b)		g decrease by 4% and $K_{R}$ decreases by 2%
c)		g increases by 4% and $K_{R}$ decreases by 4%
d)		g decrease by 2% and $K_{R}$ increases by 4%

31. A loop and a disc have the same mass and roll without slipping with the same linear velocity v. If the total kinetic energy of the loop is 8 J, the kinetic energy of the disc must be

a)		8 J
b)		6 J
c)		16 J
d)		4 J

32. A rigid body rotated about a fixed axis with variable angular velocity equal to $α - β t$ at time t where $α and β$ are constants. The angle through which it rotates before it comes to rest is

a)		$\frac{α^{2}}{2 β}$
b)		$\frac{α^{2} - β^{2}}{2 α}$
c)		$\frac{α^{2} - β^{2}}{2 β}$
d)		$\frac{α (α - β)}{2}$

33. A flywheel rolls down on an inclined plane. At any instant of time, the ration of rotational kinetic energy to total kinetic energy is

a)		1 : 2
b)		3 : 1
c)		4 : 3
d)		1 : 3

34. A homogeneous disc with a radius 0.2 m and mass 5 kg rotates around an axis passing through its centre. The angular velocity of the rotation of the disc as a function of time is given by the formula $ω = 2 + 6 t$ . The tangential force applied to the rim of the disc is

a)		1 N
b)		2 N
c)		3 N
d)		4 N

35. A light string is wound severl times around a spool of mass M and radius R. The free end of the string is attached to a fixed point and the spool is held so that the part of the string not in contact ith it is vertical. If the spool is let go, the acceleration is

a)		g/3
b)		2g/3
c)		g
d)		3g/4

36. If a rigid body rolls on a surface without slipping, then

a)		angular speed is different at different point of a rigid body
b)		linear speed is same at all points of the rigid body
c)		linear speed is minimum at the highest point but maximum at the point of contact
d)		linear speed is maximum at the highest point but minimum at the point of contact

37. A body rolls without slipping. The radius of gyration of the body about an axis passing through its centre of mass is K. If radius of the body be R, then the fraction of total energy associated with its rotational energy will be

a)		$(K^{2} + R^{2})$
b)		$(K^{2} / R^{2})$
c)		$K^{2} /$ $(K^{2} + R^{2})$
d)		$R^{2} /$ $(K^{2} + R^{2})$

38. The moment of inertia of a body about a given axis is 1.2 kg $m^{2}$ . Initially, the body is at rest. In order to produce a rotational kinetic energy of 1500 J, an angular acceleration of 25 rad/ $s^{2}$ must be applied about that axis for a duration of

a)		4s
b)		2s
c)		8s
d)		10s

39. If a particle moves in the x-y plane, the resultant angular momentum has

a)		only x- component
b)		only y- component
c)		both a and y -component
d)		only z- component

40. When a sphere rolls without slipping, the ratio of its kinetic energy of translation of its original kinetic energy is

a)		1 : 7
b)		1 : 2
c)		1 : 1
d)		5 : 7

41. The angular speed of a flywheel making 120 revolutions per minute is

a)		$π$ rad/sec
b)		2 $π$ rad/sec
c)		4 $π$ rad/sec
d)		4 $π^{2}$ rad/sec

42. If the moment of inertia of a disc about an axis tangentially and parallel to its surface be I, then the moment of inertia about the axis tangential but perpendicular to the surface will be

a)		$\frac{6}{5} I$
b)		$\frac{3}{4} I$
c)		$\frac{3}{2} I$
d)		$\frac{5}{4} I$

43. A circular disc A of radius r is made from an iron plate of thickess t and another circular disc B of radius 4r and thickess t/4. The relation between moments of inertia $I_{A}$ and $I_{B}$ is

a)		$I_{A} > I_{B}$
b)		$I_{A} = I_{B}$
c)		$I_{A} < I_{B}$
d)		depends on the actual values of t and r

44. There are four point masses m each on the corners of a aquare of side length l. What is the moment of inertia of the system about one of its diagnals?

a)		2m $l^{2}$
b)		m $l^{2}$
c)		4m $l^{2}$
d)		6m $l^{2}$

45. A cricket mat of mass 50 kg is rolled loosely in the form of a cylinder of radius 2m. Now again it is rolled tightly so that the radius becomes $\frac{3}{4}$ th of original value, then the ratio of moment of inertia of mat in the two cases is

a)		1 : 3
b)		4 : 3
c)		16 : 9
d)		3 : 5

46. Two rings of the same radius and mass are placed such that their centres are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the centre and perpendicular to the plane of one of the rings is (mass of the ring=m, radius= r)

a)		$\frac{1}{2} m r^{2}$
b)		m $r^{2}$
c)		$\frac{3}{2} m r^{2}$
d)		2m $r^{2}$

47. Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

a)		5 I
b)		3 I
c)		6 I
d)		4 I

48. A shell is fired from a gun with a muzzle velocity u m/sec at an angle $θ$ with the horizontal. At the top of trajectory, the shell explodes into two fragments P and Q of equal mass. If the speed of the fragment P immediately after explosion becomes zero, where does the centre of mass of the fragments hit the ground?

a)		$\frac{u^{2} \sin^{2} θ}{g}$
b)		$\frac{u^{2} \sin 2 θ}{g}$
c)		$\frac{u^{2} \sin^{2} θ}{2 g}$
d)		$\frac{u \sin θ}{g}$

49. Two bodies of massed 2 kg and 4 kg are moving with velocities 2 m/s and 10 m/s towards each other due to mutual gravitational attraction. What is the velocity of their centre of mass?

a)		5.3 m/s
b)		6.4 m/s
c)		zero
d)		8.1 m/s

50. A man of mass m climbs a rope of length L suspended below a balloon of mass M. The balloon is stationary with respect to ground. If the man begins to climb up the rope at a speed $V_{rel}$ (relative to rope), in what direction and with what speed (relative to ground) will the balloon move?

a)		$\vec{v} = \frac{m}{M} {\vec{v}}_{rel}$
b)		$\vec{v} = \frac{- m}{M} {\vec{v}}_{rel}$
c)		$\vec{v} = \frac{- m}{m + M} {\vec{v}}_{rel}$
d)		$\vec{v} = \frac{+ m}{m + M} {\vec{v}}_{rel}$