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. t

^{2 }

(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. (mk

^{4}r²t

^{5})/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)

7. An ideal spring with spring constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. The maximum extension in the spring is

a. 4Mg/k

b. 2Mg/k

c. Mg/k

d. Mg/2k

(JEE 2002)

Answer (b)

Solution

Change in gravitational energy = Energy stored in the spring

Mgx = ½ kx²

=> x = 2Mg/k

Revision Questions

1. A block of mass m moving at a speed v compresses a spring through a distance x before its speed is halved. Find the spring constant of the spring. (Source HC Verma, prob. 44)

2. The bob of a pendulum at rest is given a sharp hit to impart a horizontal velocity of √(10gl) where l is the length of the pendulum. Find the tension in the string when

(a) the string is horizontal

(b) the bob is at its highest point and

(c) the string makes an angle of 60° with the upward vertical

(Source HC Verma Prob 53)

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