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A round disc of moment of inertia I_{2} about its axis perpendicular to its plane and passing through its center is placed over another disc of moment of inertia I_{1} rotating with an angular velocity ω about the same axis. The final angular velocity of the combination of discs is

(A)

(B)

ω

(C)

(D)

Question-2

A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved ?

(A)

14 m/s

(B)

3 m/s

(C)

3.92 m/s

(D)

5 m/s

Question-3

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)

4 s

(B)

2 s

(C)

8 s

(D)

10 s

Question-4

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 trough a point on its rim will be

(A)

5 I

(B)

3 I

(C)

6 I

(D)

4 I

Question-5

A spherical ball rolls on a table without slipping. Then the fraction of its total energy associated with rotation is

(A)

^{2}/5

(B)

^{2}/7

(C)

^{3}/5

(D)

^{3}/7

Question-6

A cart of mass M is tied to one end of a massless rope of length 10 m. The other end of the rope is in the hands of a man of mass M. The entire system is on a smooth horizontal surface. The man is at x = 0 and the car at x = 10 m. If the man pulls the cart by the rope, the man and the cart will meet at the point.

(A)

They will never meet

(B)

x = 10 m

(C)

x = 5 m

(D)

x = 0

Question-7

ABC is a right angled triangular plate of uniform thickness. The sides are such that AB > BC as shown in figure. I_{1} , I_{2}, I_{3} are moments of inertia about AB, BC and AC respectively. Then which of the following relations is correct ?

(A)

I_{1} = I_{2} = I_{3}

(B)

I_{2} > I_{1} > I_{3}

(C)

I_{3} < I_{2} < I_{1}

(D)

I_{3} > I_{1} > I_{2 }

Question-8

If a sphere is rolling, the ratio of the translational energy to total kinetic energy is given by

(A)

7 : 10

(B)

2 : 5

(C)

10 : 7

(D)

5 : 7

Question-9

A particle of mass M is revolving along a circle of radius R and another particle of mass m is revolving in a circle of radius r. If time periods of both particles are same, then the ratio of their angular velocities is

(A)

1

(B)

^{R}/r

(C)

^{r}/R

(D)

Question-10

Two racing cars of masses m and 4m are moving in circles of radii r and 2r respectively. If their speeds are such that each makes a complete circle in the same time. Then the ratio of the angular speeds of the first to the second car is

(A)

8 : 1

(B)

4 : 1

(C)

2 : 1

(D)

1 : 1

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