Work and Energy Past JEE Questions

1. A body is moved along a straight line by a machine delivering constant power. The distance moved by the body in time t is proportional to

a. t^1/2
b. t^3/4
c. t^3/2
d. t²

(1984)

2. A uniform chain of length L and mass M is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part on to the table is:

a. MgL
b. MgL/3
c. MgL/9
d. MgL/18

(1985)

3. A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that:

a. its velocity is constant.
b. its acceleration is constant
c. its kinetic energy is constant
d. it moves in a circular path

(1987)

4. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with t as ac = k²rt² where k is a constant. The power delivered to the particle by the force acting on it is

a. 2 πmk²r²t
b. mk²r²t
c. (mk⁴r²t⁵)/3
d. zero

(1994)

5. 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. 0.7 m form 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)

6. A force F = -K(yi + xj) (where K is a positive constant) acts on a particle moving in the xy plane. Starting from the origin, the particle is taken along the positive x axis to the point (a,0) and then parallel to the y axis to the point (a,a). The total work done by the force F on the particle is

a. -2Ka²
b. 2Ka²
c. -Ka²
d. Ka²

(1998)

solutions some time later