Work Power & Energy

A body of mass $2 \mathrm{~kg}$ is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in $4 \mathrm{~s}$ is $\frac{1}{3} \alpha^{2} \sqrt{P} m$. The value of $\alpha$ w...

A 0.4 kg mass takes 8s to reach ground when dropped from a certain height 'P' above surface of earth. The loss of potential energy in the last second of fall is __________ J.
(Take g = 10 m/s\(^2\))

A stone is projected at angle \(30^{\circ}\) to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be -

Identify the correct statements from the following :
A. Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket is negative.
B. Work done by gravitational force in lifting a bucket out of a well by a rope ...

An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under the action of force F = 2N. In the process of its linear motion, the angle \(\theta\) (as shown in figure) between the direction of force and horizonta...

A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of \(\mathrm{5^{th}}\) second. The force acted on the body is ________ N.

A body of mass 1kg begins to move under the action of a time dependent force \(\overrightarrow F = \left( {t\widehat i + 3{t^2}\,\widehat j} \right)\) N, where \(\widehat i\) and \(\widehat j\) are the unit vectors along \(x\) and \(y\) ax...

A small particle moves to position \(5 \hat{i}-2 \hat{j}+\hat{k}\) from its initial position \(2 \hat{i}+3 \hat{j}-4 \hat{k}\) under the action of force \(5 \hat{i}+2 \hat{j}+7 \hat{k} \mathrm{~N}\). The value of work done will be _________...

A force \(\mathrm{F}=\left(5+3 y^{2}\right)\) acts on a particle in the \(y\)-direction, where \(\mathrm{F}\) is in newton and \(y\) is in meter. The work done by the force during a displacement from \(y=2 \mathrm{~m}\) to $$y=5 \mathrm{~m}...

A block is fastened to a horizontal spring. The block is pulled to a distance \(x=10 \mathrm{~cm}\) from its equilibrium position (at \(x=0\)) on a frictionless surface from rest. The energy of the block at \(x=5\) \(\mathrm{cm}\) is $$0.25...

A block of mass $10 \mathrm{~kg}$ is moving along $\mathrm{x}$-axis under the action of force $F=5 x~ N$. The work done by the force in moving the block from $x=2 m$ to $4 m$ will be __________ J.

Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is :

The ratio of powers of two motors is \(\frac{3 \sqrt{x}}{\sqrt{x}+1}\), that are capable of raising \(300 \mathrm{~kg}\) water in 5 minutes and \(50 \mathrm{~kg}\) water in 2 minutes respectively from a well of \(100 \mathrm{~m}\) deep. The...

A car accelerates from rest to \(u \mathrm{~m} / \mathrm{s}\). The energy spent in this process is E J. The energy required to accelerate the car from \(u \mathrm{~m} / \mathrm{s}\) to \(2 \mathrm{u} \mathrm{m} / \mathrm{s}\) is $$\mathrm{n...

To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the engine of the bus will be ____________ KJ. [The coefficient of friction between tyre of bus and road is 0.04.]

Given below are two statements:
Statement I : A truck and a car moving with same kinetic energy are brought to rest by applying breaks which provide equal retarding forces. Both come to rest in equal distance.
Statement II : A car moving to...

A force \(\vec{F}=(2+3 x) \hat{i}\) acts on a particle in the \(x\) direction where F is in newton and \(x\) is in meter. The work done by this force during a displacement from \(x=0\) to \(x=4 \mathrm{~m}\), is __________ J.

A block of mass \(5 \mathrm{~kg}\) starting from rest pulled up on a smooth incline plane making an angle of \(30^{\circ}\) with horizontal with an affective acceleration of \(1 \mathrm{~ms}^{-2}\). The power delivered by the pulling force ...

A closed circular tube of average radius 15 cm, whose inner walls are rough, is kept in vertical plane. A block of mass 1 kg just fit inside the tube. The speed of block is 22 m/s, when it is introduced at the top of tube. After completing ...

If the maximum load carried by an elevator is \(1400 \mathrm{~kg}\) ( \(600 \mathrm{~kg}\) - Passengers + 800 \(\mathrm{kg}\) - elevator), which is moving up with a uniform speed of \(3 \mathrm{~m} \mathrm{~s}^{-1}\) and the frictional forc...

A particle of mass 500 gm is moving in a straight line with velocity v = b x5/2. The work done by the net force during its displacement from x = 0 to x = 4 m is : (Take b = 0.25 m\(-\)3/2 s\(-\)1).

In the given figure, the block of mass m is dropped from the point 'A'. The expression for kinetic energy of block when it reaches point 'B' is

A ball is projected with kinetic energy E, at an angle of \(60^{\circ}\) to the horizontal. The kinetic energy of this ball at the highest point of its flight will become :

A block of mass '\(\mathrm{m}\)' (as shown in figure) moving with kinetic energy E compresses a spring through a distance \(25 \mathrm{~cm}\) when, its speed is halved. The value of spring constant of used spring will be $$\mathrm{nE} \,\,\...

A bullet of mass \(200 \mathrm{~g}\) having initial kinetic energy \(90 \mathrm{~J}\) is shot inside a long swimming pool as shown in the figure. If it's kinetic energy reduces to \(40 \mathrm{~J}\) within \(1 \mathrm{~s}\), the minimum len...

Sand is being dropped from a stationary dropper at a rate of \(0.5 \,\mathrm{kgs}^{-1}\) on a conveyor belt moving with a velocity of \(5 \mathrm{~ms}^{-1}\). The power needed to keep the belt moving with the same velocity will be :

Arrange the four graphs in descending order of total work done; where W1, W2, W3 and W4 are the work done corresponding to figure a, b, c and d respectively.

As per the given figure, two blocks each of mass \(250 \mathrm{~g}\) are connected to a spring of spring constant \(2 \,\mathrm{Nm}^{-1}\). If both are given velocity \(v\) in opposite directions, then maximum elongation of the spring is :

A 0.5 kg block moving at a speed of 12 ms\(-\)1 compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be _______________ Nm\(-\)1.

A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the m...

A body of mass \(0.5 \mathrm{~kg}\) travels on straight line path with velocity \(v=\left(3 x^{2}+4\right) \mathrm{m} / \mathrm{s}\). The net workdone by the force during its displacement from \(x=0\) to \(x=2 \mathrm{~m}\) is :

A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms\(-\)1 gets embedded in it, then loss of kinetic energy will be :

A ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance \({h \over 2}\). The spring constan...

A particle experiences a variable force \(\overrightarrow F = \left( {4x\widehat i + 3{y^2}\widehat j} \right)\) in a horizontal x-y plane. Assume distance in meters and force is newton. If the particle moves from point (1, 2) to point (2,...

A block moving horizontally on a smooth surface with a speed of 40 ms\(-\)1 splits into two equal parts. If one of the parts moves at 60 ms\(-\)1 in the same direction, then the fractional change in the kinetic energy will be x : 4 where x ...

A block moving horizontally on a smooth surface with a speed of 40 m/s splits into two parts with masses in the ratio of 1 : 2. If the smaller part moves at 60 m/s in the same direction, then the fractional change in kinetic energy is :-

A small block slides down from the top of hemisphere of radius R = 3 m as shown in the figure. The height 'h' at which the block will lose contact with the surface of the sphere is __________ m.(Assume there is no friction between the block...

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that Emech = 8 J, the incorrect statement for this system is :
[...

Two persons A and B perform same amount of work in moving a body through a certain distance d with application of forces acting at angle 45\(^\circ\) and 60\(^\circ\) with the direction of displacement respectively. The ratio of force appli...

A uniform chain of length 3 meter and mass 3 kg overhangs a smooth table with 2 meter lying on the table. If k is the kinetic energy of the chain in joule as it completely slips off the table, then the value of k is ................. . (Tak...

A force of F = (5y + 20)\(\widehat j\) N acts on a particle. The work done by this force when the particle is moved from y = 0 m to y = 10 m is ___________ J.

The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as \(U = {\alpha \over {{r^{10}}}} - {\beta \over {{r^5}}} - 3\)where, \(\alpha\) and \(\beta\) are positive constants. The equilibrium di...

A porter lifts a heavy suitcase of mass 80 kg and at the destination lowers it down by a distance of 80 cm with a constant velocity. Calculate the work done by the porter in lowering the suitcase.(take g = 9.8 ms\(-\)2)

In a spring gun having spring constant 100 N/m a small ball 'B' of mass 100 g is put in its barrel (as shown in figure) by compressing the spring through 0.05 m. There should be a box placed at a distance 'd' on the ground so that the ball ...

A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time 't' is proportional to :

An engine is attached to a wagon through a shock absorber of length 1.5 m. The system with a total mass of 40,000 kg is moving with a speed of 72 kmh\(-\)1 when the brakes are applied to bring it to rest. In the process of the system being ...

A body of mass 'm' dropped from a height 'h' reaches the ground with a speed of 0.8\(\sqrt {gh}\). The value of workdone by the air-friction is :

A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time 't' is proportional to :-

As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed of the particle at B is x m/s. (Take g = 10 m/s2)The value of...