Work Power & Energy

A student skates up a ramp that makes an angle 30\(^\circ\) with the horizontal. He/she starts (as shown in the figure) at the bottom of the ramp with speed v0 and wants to turn around over a semicircular path xyz of radius R during which h...

A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted wit...

A particle is moved along a path AB-BC-CD-DE-EF-FA, as shown in figure, in presence of a force \(F = (\alpha y\widehat i + 2\alpha x\widehat j)\) N, where x and y are in meter and \(\alpha\) = \(-\)1 Nm-1. The work done on the particle b...

In the List-\({\rm I}\) below, four different paths of a particle are given as functions of time. In these functions, \(\alpha\) and \(\beta\) are positive constants of appropriate dimensions and \(\alpha \ne \beta\) In each case, th...

A particle of mass \(m\) is initially at rest at the origin. It is subjected to a force and starts moving along the \(x\)-axis. Its kinetic energy \(K\) changes with time as \(dK/dt = \gamma t,\) where \(\gamma\) is a positive constant of ...

A spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is \(2.0\,N{m^{ - 1}}\) and the mass of the block is \(2.0\) \(kg.\) Ignore the mass of the spring. Initially the spring is an unstretched ...

A flat plate is moving normal to its plane through a gas under the reaction of a constant force \(F.\) The gas is kept at a very low pressure. The speed of the plate \(v\) is much less than the average speed u of the gas molecules.
Which o...

A particle of unit mass is moving along the x-axis under the
influence of a force and its total energy is conserved. Four
possible forms of the potential energy of the particle are given
in Column I (a and U0
are constants). Match the pote...

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of t...

Consider an elliptically shaped rail PQ in the vertical plane with
OP = 3 m and OQ = 4 m. A block of mass 1 kg is pulled along the
rail from P to Q with a force of 18 N, which is always parallel to
line PQ (see the figure given). Assuming n...

The magnitude of the normal reaction that acts on the block at the point Q is

The speed of the block when it reaches the point Q is

A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to
the particle. If the initial speed (in m/s) of the particle is zero, the speed (in m/s) after 5 s is

The work done on a particle of mass m by a force
\($K\left[ {{x \over {{{\left( {{x^2} + {y^2}} \right)}^{3/2}}}}\widehat i + {y \over {{{\left( {{x^2} + {y^2}} \right)}^{3/2}}}}\widehat j} \right]\)$
(K being a constant of appropriate dime...

A bob of mass m, suspended by a string of length l1 is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of leng...

A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The
coefficient of friction between the block and the floor is 0.1. Initially the
block is at rest and the spring is un-stretched. An impulse is given to the
block as ...

A thin ring of mass 2 kg and radius 0.5 m is rolling without on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction hits the ring at a height of 0.75 m and goes vertical...

A block of mass 2 kg is free to move along the x-axis. It is at rest and from t = 0 onwards, it is subjected to a time-dependent force F(t) in the x-direction. The force F(t) varies with t as shown in the figure. The kinetic energy of the b...

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B ma...

A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.36 kg and 0.72 kg. Taking g = 10 m/s2, find the work done (in joules) by the string on the block of mass 0.36 kg during ...

A bob of mass M is suspended by a massless string of length L. The horizontal velocity V at position A is just sufficient to make it reach the point B. The angle \(\theta\) at which the speed of the bob is half of that at A, satisfies,

A block (B) is attached to two unstretched springs S1 and S2 with spring constants k and 4k respectively (see figure I). The other ends are attached to identical supports M1 and M2 not attached to the walls. The springs and supports have ne...

Statement 1 :
A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30$$...

There is a rectangular plate of mass M kg of dimensions ( $a \times b$ ). The plate is held in horizontal position by striking $n$ small balls each of mass m per unit area per unit time. These are striking in the shaded half region of the p...

A ball moves over a fixed track as shown in the figure. From $A$ to $B$, the ball rolls without slipping. Surface $B C$ is frictionless. $K_A, K_B$ and $K_c$ are kinetic energies of the ball at $A, B$ and C , respectively. Then

A particle is acted by a force F = kx, where k is a +ve constant. Its potential energy at x = 0 is zero. Which
curve correctly represents the variation of potential energy of the block with respect to x

If 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.

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. Then the maximum extension in the spring is

A wind-powered generator converts wind energy into electrical 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 wil...

A 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 force \(F = - K\left( {y\widehat i + x\widehat j} \right)\) (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 $$\left( {a,0}...

A stone tied to a string of 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 lowest position, and has a speed u. The magnitude of the change in its ve...

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration \({a_c}\) is varying with time t as \({a_c}\) = k2rt2 where k is a constant. The power delivered to the perticles by the force act...

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 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 t...

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

Two masses of 1gm and 4 gm are moving with equal kinetic energies. The ratio of the magnitude of their linear momentum is

If a machine is lubricated with oil