A small object of uniform density rolls up a curved surface with an initial velocity v'. It reaches up to a maximum height of 3v2/4g with respect to the initial position. The object is

(a) ring

(b) solid sphere

(c) hollow sphere

(d) disc

Concept Questions :-

Moment of inertia
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When a mass is rotating in a plane about a fixed point, its angular momentum is directed along

(a)a line perpendicular to the plane of rotation

(b)the line making an angle of 45° to the plane of rotation

(c)the radius

(d)the tangent to the orbit

Concept Questions :-

Angular momentum
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Two persons of mass 55 kg and 65 kg respectively, are at the opposite ends of a boat.The length of the boat is 3.0m and weighs 100 kg.The 55 kg man walks up to the 65 kg man and sits with him.If the boat is in still water the centre of mass of the system shifts by 

(a)3.0m                            (b)2.3m

(c)zero                             (d)0.75m

Concept Questions :-

Center of mass
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A solid cylinder of mass 3kg is rolling on a horizontal surface with velocity 4 ms-1. It collides with a horizontal spring of force constant 200 Nm-1. The maximum compression produced in the spring will be

1. 0.5 m

2. 0.6 m

3. 0.7 m

4. 0.2 m

Concept Questions :-

Rolling motion
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Two spheres A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v2 in a direction perpendicular to the original direction.The mass A moves after collision in the direction

(a)same as that of B

(b)opposite to that of B

(c)θ=tan-112to the xaxis

(d)θ=tan-1-12to the xaxis

Concept Questions :-

Linear momentum
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The moment of inertia of a uniform circular

disc is maximum about an axis perpendicular

to the disc and passing through

(a) B                    (b) C

(c) D                    (d) A

Concept Questions :-

Moment of inertia
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Three masses are placed on the x-axis:

300 g at origin, 500 g at x= 40 cm and 400g

at x=70 cm. The distance of the center of

mass from the origin is 

(a) 40 cm                   (b) 45 cm

(c) 50 cm                   (d) 30 cm 

Concept Questions :-

Center of mass
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The instantaneous angular position of a point on

a rotating wheel is given by the equation

θ(t)=2t3-6t2

The torque on the wheel becomes zero at

(a) t=0.5 s

(b) t=0.25 s

(c) t=2 s

(d) t=1 s

Concept Questions :-

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The moment of inertia of a thin uniform rod of 

mass M and length L about an axis passing

through its mid-point and perpendicular to its

length is I0. Its moment of inertia about an 

axis passing through one of its ends and

perpendicular to its length is

(a) I0+ML2/4

(b) I0+2ML2

(c) I0+ML2

(d) I0+ML2/2

Concept Questions :-

Moment of inertia
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A body of mass M hits normally a rigid wall with velocity v and bounces back with the same velocity. The impulse experienced by the body is

(a) 1.5 Mv                                                 (b) 2 Mv

(c) zero                                                     (d) Mv

Concept Questions :-

Linear momentum
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