Past JEE Fill in the Blanks – Circular Motion and Related Chapters

1. A particle moves in a circle of radius R. In half the period of revolution, its displacement is ___________ and the distance covered is _______________. (1983)

2. The numerical value of the angular velocity of rotation of the earth should be __________ rad/s in order to make the effective acceleration due to gravity equal to zero at the equator. (1984)

3. A uniform cube of side ‘a’ and mass ‘m’ rests on a rough horizontal table. A horizontal force F is applied normal to one of the faces at a point that is directly above the centre of the face, at a height 3a/4 above the base. The minimum value of F for which the cube begins to tip about an edge is _________. (Assume that the cube does not slide). (1984)

4. According to Kepler’s second law, the radius vector to a planet from the sun sweeps out equal areas in equal intervals of time. This law is a consequence of the conservation of ____________. (1985)

5. A spotlight S rotates in horizontal plane with a constant angular velocity of 0.1 rad/s. The spot of light P moves along the wall at distance of 3 m. The velocity of spot P when θ = 45° is ___________ m/s. (1987)

6. A geostationary satellite is orbiting the earth at a height of 6R above the surface of the earth, where R is the radius of the earth. The time period of another satellite at a height of 2.5R from the surface of the earth is ___________ hours. (1987)

7. A cylinder of mass ‘M’ and radius ‘R’ is resting on a horizontal platform (which is parallel to the x-y plane) with its axis fixed along the y-axis and free to rotate about its axis. The platform is given a motion in the x-direction given as x = A cos ωt. There is no slipping between the cylinder and the platform. The maximum torque acting on the cylinder during its motion is ___________________. (1988)

8. A stone of mass ‘m’ tied to the end of a string, is whirled around in a horizontal circle. (Neglect the force due to gravity). The length of the string is reduced gradually keeping the angular momentum of the stone about the centre of the circle constant. Then, the tension in the string is given by T = Arⁿ where A is a constant, r is the instantaneous radius of the circle, and n = _____________. (1993)

9. The ratio of Earth’s orbital angular momentum (about the Sun) to its mass is 4.4*10¹⁵ m²/s. The area enclosed by the Earth’s orbit is approximately ___________ m². (1997 cancelled)