Give the correct answer/choice

1. A thin circular ring of mass ‘M’ and radius ‘r’ is rotating about its axis with a constant angular velocity ω. Two objects, each of mass m, are attached gently to the opposite ends of a diameter of the ring. The wheel now rotates with an angular velocity

a. ω M/(M+m)

b. ω(M-2m)/(M+2m)

c. ω M/(M+2m)

d. ω (M+2m)/M

(1983)

2. A satellite is launched into a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The period of the second satellite is larger than the first one by approximately.

a. 0.7%

b. 1%

c. 1.5%

d. 3.0%

(1995)

3. Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is located at a distance of

a. 0.42 m from mass of 0.3 kg

b. 0.70 m from mass of 0.7 kg

c. 0.98 m from mass of 0.3 kg

d. 0.98 m from mass of 0.7 kg

(1995)

4. If the distance between the earth and the sun were half its present value, the number of days in a year would have been

a. 64.5

b. 129

c. 182.5

d. 730

**Revision Questions**

1. A circular road of radius r is banked for a speed of v = 40 km/hr. A car of mass m attempts to go on the circular road. The friction coefficient between the tyre and the road is negligible.

a. The car cannot make a turn without skidding.

b. If the car turns at a speed less than 40 km/hr, it will slip down.

c. If the car turns at the correct speed of 40 km/hr, the force by the road on the car is equal to mv²/r.

d. If the car turns at the correct speed of 40 km/hr, the force by the road on the car is greater than mg as well as greater than mv²/r.

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