Work Power & Energy

A ball of mass 4 kg, moving with a velocity of 10 ms\(-\)1, collides with a spring of length 8 m and force constant 100 Nm\(-\)1. The length of the compressed spring is x m. The value of x, to the nearest integer, is ____________.

A boy is rolling a 0.5 kg ball on the frictionless floor with the speed of 20 ms-1. The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now?

Consider a force \(\overrightarrow F = - x\widehat i + y\widehat j\)
. The work done
by this force in moving a particle from point
A(1, 0) to B(0, 1) along the line segment is :
(all quantities are in SI units)

A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg. If the frictional force on the elevator is 4000 N, the speed of the elevator at full load is close to : (1 HP = 746 W, g = 10 ms-2)

A particle (m = 1 kg) slides down a frictionless track (AOC) starting from rest at a point A (height 2 m). After reaching C, the particle continues to move freely in air as a projectile. When it reaching its highest point P (height 1 m), th...

An elevator in a building can carry a maximum of 10 persons, with the average mass of each
person being 68 kg, The mass of the elevator itself is 920 kg and it moves with a constant speed
of 3 m/s. The frictional force opposing the motion i...

If the potential energy between two molecules is given by
U = \(- {A \over {{r^6}}} + {B \over {{r^{12}}}}\),
then at equilibrium,
separation between molecules, and the potential energy are :

A body of mass 2 kg is driven by an engine
delivering a constant power of 1 J/s. The body
starts from rest and moves in a straight line.
After 9 seconds, the body has moved a
distance (in m) _______.

A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a
distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with
distance to 100 N. The total distance th...

A cricket ball of mass 0.15 kg is thrown
vertically up by a bowling machine so that it
rises to a maximum height of 20 m after leaving
the machine. If the part pushing the ball applies
a constant force F on the ball and moves
horizontally a...

A particle is moving unidirectionally on a horizontal plane under the action of a constant power
supplying energy source. The displacement (s) - time (t) graph that describes the motion of the
particle is (graphs are drawn schematically and...

A block starts moving up an inclined plane of inclination 30o with an initial velocity of v0
. It comes
back to its initial position with velocity \({{{v_0}} \over 2}\). The value of the coefficient of kinetic friction between
the block and...

A small block starts slipping down from a point
B on an inclined plane AB, which is making an angle \(\theta\) with the horizontal section BC is
smooth and the remaining section CA is rough
with a coefficient of friction \(\mu\). It is f...

A block of mass m, lying on a smooth horizontal surface, is attached to a sring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium posit...

A force acts on a 2 kg object so that its position is given as a function of time as x = 3t2 + 5. What is the work done by this force in first 5 seconds ?

A uniform cable of mass 'M' and length 'L' is
placed on a horizontal surface such that its (1/n)th
part is hanging below the edge of the
surface. To lift the hanging part of the cable upto
the surface, the work done should be :

A particle moves in one dimension from rest
under the influence of a force that varies with
the distance travelled by the particle as shown
in the figure. The kinetic energy of the particle
after it has travelled 3m is :

A block of mass m is kept on a platform which starts from rest with constant acceleration g/2 upward, as shown in figure. Work done by normal reaction on block in time is -

A particle which is experiencing a force, given by \(\overrightarrow F = 3\widehat i - 12\widehat j,\) undergoes a displacement of \(\overrightarrow d = 4\overrightarrow i\) particle had a kinetic energy of 3 J at the beginning of the di...

Two particles of the same mass m are moving in circular orbits because of force, given by \(F\left( r \right) = {{ - 16} \over r} - {r^3}\)
The first particle is at a distance r = 1, and the second, at r = 4. The best estimate for the ratio...

A body of mass m starts moving from rest along x-axis so that its velocity varies as \(\upsilon = a\sqrt s\) where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on the body in the ...

A particle is moving in a circular path of radius \(a\) under the action of an attractive potential \(U = - {k \over {2{r^2}}}\) Its total energy is:

An object is dropped from a height h from the ground. Every time it hits the ground it looses 50% of its kinetic energy. The total distance covered as t \(\to\) \(\infty\) is :

A body of mass m = 10–2 kg is moving in a medium and experiences a frictional force F = –kv2. Its initial speed is v0 = 10 ms–1. If, after 10 s, its energy is \({1 \over 8}mv_0^2\), the value of k will be:

A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done
by the force during the first 1 sec. will be:

A car of weight W is on an inclined road that rises by 100 m over a distance of 1 km
and applies a constant frictional force \({W \over 20}\) on the car. While moving uphill on the road at a speed of 10 ms−1, the car needs power P. If it ne...

Velocity-time graph for a body of mass 10 kg is shown in figure. Work-done on
the body in first two seconds of the motion is :

A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n2 R t2 where n is a constant. The power delivered to the particle by the force acting on it, is :

A point particle of mass \(m,\) moves long the uniformly rough track \(PQR\) as shown in the figure. The coefficient of friction, between the particle and the rough track equals \(\mu .\) The particle is released, from rest from the point $...

A person trying to lose weight by burning fat lifts a mass of \(10\) \(kg\) upto a height of \(1\) \(m\) \(1000\) times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up conside...

When a rubber-band is stretched by a distance \(x\), it exerts restoring force of magnitude \(F = ax + b{x^2}\) where \(a\) and \(b\) are constants. The work done in stretching the unstretched rubber-band by \(L\) is :

This question has Statement \(1\) and Statement \(2.\) Of the four choices given after the Statements, choose the one that best describes the two Statements.
If two springs \({S_1}\) and \({S_2}\) of force constants \({k_1}\) and \({k_2}\)...

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by \(U\left( x \right) = {a \over {{x^{12}}}} - {b \over {{x^6}}},\) where \(a\) and \(b\) are constants and \(x\) is the distance b...

An athlete in the olympic games covers a distance of \(100\) \(m\) in \(10\) \(s.\) His kinetic energy can be estimated to be in the range

A particle is projected at \(60^\circ\) to the horizontal with a kinetic energy K. The kinetic energy at the
highest point is

A \(2\) \(kg\) block slides on a horizontal floor with a speed of \(4m/s.\) It strikes a uncompressed spring, and compress it till the block is motionless. The kinetic friction force is \(15N\) and spring constant is \(10, 000\) \(N/m.\) Th...

A ball of mass \(0.2\) \(kg\) is thrown vertically upwards by applying a force by hand. If the hand moves \(0.2\) \(m\) while applying the force and the ball goes upto \(2\) \(m\) height further, find the magnitude of the force. (consider $...

The potential energy of a \(1\) \(kg\) particle free to move along the \(x\)-axis is given by \(V\left( x \right) = \left( {{{{x^4}} \over 4} - {{{x^2}} \over 2}} \right)J\).
The total mechanical energy of the particle is \(2J.\) Then, the ...

A particle of mass \(100g\) is thrown vertically upwards with a speed of \(5\) \(m/s\). The work done by the force of gravity during the time the particle goes up is

A mass of \(M\) \(kg\) is suspended by a weightless string. The horizontal force that is required to displace it until the string makes an angle of \({45^ \circ }\) with the initial vertical direction is

The upper half of an inclined plane with inclination \(\phi\) is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half i...

A spherical ball of mass \(20\) \(kg\) is stationary at the top of a hill of height \(100\) \(m\). It rolls down a smooth surface to the ground, then climbs up another hill of height \(30\) \(m\) and finally rolls down to a horizontal base...

A body of mass \(m\) is accelerated uniformly from rest to a speed \(v\) in a time \(T.\) The instantaneous power delivered to the body as a function of time is given by

A bullet fired into a fixed target loses half of its velocity after penetrating \(3\) \(cm.\) How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement \(x\) is proportional to

A body of mass \(' m ',\) acceleration uniformly from rest to \('{v_1}'\) in time \({T}\). The instantaneous power delivered to the body as a function of time is given by

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 particles takes place in a plane. It follows that

A uniform chain of length \(2\) \(m\) is kept on a table such that a length of \(60\) \(cm\) hangs freely from the edge of the table. The total mass of the chain is \(4\) \(kg.\) What is the work done in pulling the entire chain on the tab...

A force \(\overrightarrow F = \left( {5\overrightarrow i + 3\overrightarrow j + 2\overrightarrow k } \right)N\) is applied over a particle which displaces it from its origin to the point $$\overrightarrow r = \left( {2\overrightarrow i ...

A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time \('t'\) is proportional to