IIT JEE -PHYSICS

Work, Power, and Energy

SECTION – I

OBJECTIVE QUESTIONSOnly one option is correct

01Two masses of 1 g and 4 g are moving with equal kinetic energies. The ratio of

the magnitude of their momenta is :

a. 4 : 1

b. √2: 1

c. 1 : 2

d. 1 : 16

Problem1980

02A 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. t1/2

b. t3/4

c. t3/2

d. t2

Problem1984

03A 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 the

table is :

a. MgL

b. MgL/3

c. MgL/9

d. MgL/18

Problem1985

04A particle of mass m is moving in a circular path of constant radius r such that its

centripetal acceleration ac is varying with time t as ac = k2 rt2, where k is a

constant the power delivered to the particle by the force acting on it is:

a. 2πmk2r2

b. mk2r2t

c. (mk4r2t5)/3

d. zero

Problem1994

05A stone tied to a sting or length L is whirled in a vertical circle with the other end

of the string at the center. At a certain instant of time, the stone is at its lower

position, and has a speed u. the magnitude of the change in its velocity as it

reaches a position where the string is horizontal is :

Problem1998

06A force (where K is a positive constant) acts on a particle moving in

the x-y plane. Starting form 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. -2 Ka2

b. 2 Ka2

c. - Ka2

d. Ka2

Problem1998

ˆ ˆ( )F yi xj

07A spring of force- constant K is cut into two pieces such that one piece is double

the length of the other. Then the long piece will have a force-constant of :

a. (2/3)k

b. (3/2)k

c. 3 k

d. 6 k

Problem1999

08A wind-powered generator converts wind energy into electric energy. Assume

that the generator converts a fixed fraction of the wind energy intercepted by its

blades into electrical energy. For wind speed v, the electrical power output will be

proportional to :

a. v

b. v2

c. v3

d. v4

Problem2001

09A particle, which is constrained to move along x-axis, is subjected to a force in the

same direction which varies with the distance x of the particle from the origin as

F(x) = - kx + ax3. Here, k and a are positive constant. For x 0, the functional form of

the potential energy U(x) of the particle is :

Problem2002

10An 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. Then the maximum extension in the spring is:

Problem2002

11A simple pendulum is oscillating without damping. When the displacement of the

bob is less than maximum, its acceleration vector a is correctly shown in :

Problem2002

12If W1, W2 and W3 represent the work done in moving a particle from A to B along

three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of

a point mass m. find the correct relation between W1, W2 and W3 :

W1 > W2 > W3

W1 = W2 = W3

W1 < W2 < W3

W2 > W1 > W3

Problem2003

13A particle is placed at the origin and a force F = kx is acting on it (where k is a

positive constant). If U (0) = 0, the graph of U (x) versus x will be (where U is the

potential energy function) :

Problem2004

SECTION – II

OBJECTIVE QUESTIONSMore than one options are correct

01A 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 acceleration is constant

d. It moves in a circular path

Problem1987

SECTION – III

SUBJECTIVE QUESTIONS

01In the figures (a) and (b) AC, DG and GF are fixed inclined planes, BC = EF = x and

AB = DE = y. A small block of mass M is released from the point A. Its slides down

AC and reaches C with a speed Vc. The same block is released from rest from the

point D. Its slides down DGF and reaches the point F with speed VF. The

coefficients

Of kinetic frictions between block and both the surfaces AC and DGF are .

Calculate VC and VF.

Problem1980

02A body of mass 2 kg is being dragged with a uniform velocity of 2 m/s on a rough

horizontal plane. The coefficient of friction between the body and the surface is

0.20, J = 4.2 J/cal and g =9.8 m/s2. Calculate the amount of heat generated in 5

sec.

Problem1980

03A led bullet just melts when stopped by an obstacle Assuming that 25 per cent of

the heat is absorbed by the obstacle, find the velocity of the bullet if its initial

temperature is 270C.

(Melting point of lead = 3270 C, specific heat of lead = 0.03 cal/g-C0, latent heat of

fusion of lead = 6 cal/g-0C, J = 4.2 Joule/calorie).

Problem1981

04Two blocks A and B are connected to each other by a string and a spring; the

string passes over a frictionless pulley as shown in figure. Block B slides over the

horizontal top surface of a stationary block C and the block A slides along the

vertical side of C, both with the same uniform speed. The coefficient of friction

between the surfaces of blocks is 0.2. Force constant of the spring is 1960 N/m. If

mass of block A is 2 kg. Calculate the mass of block B and the energy stored in the

spring.

Problem1993

05A 0.5 kg block slides from the point A (see fig.) on a horizontal track with an initial

speed of 3 m/s towards a weightless horizontal spring of length 1 m and force

constant 2 N/m. the part AB of the track is frictionless and the part BC has the

coefficients of static and kinetic friction as 0.22 and 0.2 respectively. If the

distances AB and BD are 2 m and 2.14 m respectively, find the total distance

through which the block moves before it comes to rest completely.(Take g =10

m/s2).

Problem1983

06A string, with one end fixed on a rigid wall, passing over a fixed frictionless pulley

at a distance of 2 m from the wall, has a point mass M = 2 kg attached to it at a

distance of 1 m from the wall. A mass m = 0.5 kg attached at the free end is held

at rest so that the string is horizontal between the wall and the pulley and vertical

beyond the pulley. What will be the speed with which the mass M will hit the wall

when the mass m is released?

Problem1985

07A bullet of mass M is fired with a velocity 50 m/s at an angle θ with the

horizontal. At the highest point of its trajectory, it collides head-on with a bob of

mass 3 M suspended by a massless string of length 10/3 metres and gets

embedded in the bob. After the collision the string move through an angle of

1200. Find :

a. The angle θ,

b. The vertical and horizontal co-ordinates of the initial position of the bob

with respect to the point of firing of the bullet. (Take g = 10 m/s2)

Problem1988

08A particle is suspended vertically from a point O by an inextensible massless

string of length L. A vertical line AB is at a distance L/8 from O as shown in figure.

The object is given a horizontal velocity u. At some point, its motion ceases to be

circular and eventually the object passes through the line AB. At the instant of

crossing AB< its velocity is horizontal. Find u.

Problem1999

u

09A spherical ball of mass m is kept at the highest point in the space between two fixed, concentric spheres A and B (see figure). The smaller sphere A has a radius R and the space between the two spheres has a width d. The ball has a diameter very slightly less then d. All surfaces are frictionless. The ball is given a gentle push(towards the right in the figure). The angle made by the radius vector of the ball with the upward vertical is denoted by θ.Express the total normal reaction force exerted by the spheres on the ball as a function of a angle θ. Let NA and NB denote the magnitudes of the normal reaction forces on the ball exerted by the spheres A and B, respectively. Sketch the variations of NA and NB as function of cos θ in the range 0≤θ≤π by drawing two separate graphs in your answer book, taking cosθ on the horizontal axis.

Problem2004

10Two identical ladders are arranged as shown in the figure. Mass of each ladder is

M and length L. The system is in equilibrium. Find direction and magnitude of

frictional force acting at A or B.

Problem2005

11A circular disc with a groove along its diameter is placed horizontally. A block of

mass 1 kg is placed as shown. The coefficient of friction between the block and all

surfaces of groove in contact is μ=2/5. The disc has an acceleration of 25 m/s2.

Find the acceleration of the block with respect of disc.

Problem2006