Work-energy-power practice · Mixed difficulty

A particle of mass $\mathrm{m}_1$ collides head-on with another stationary particle of mass $\mathrm{m}_2\left(\mathrm{m}_2 > \mathrm{m}_1\right)$. The collision is perfectly inelastic. The fraction of kinetic energy which is converted into heat in this collision is

A car is moving along a circular path of radius $500 {~m}$ with a speed of $30 {~ms}^{-1}$. If at some instant, its speed increases at the rate of $2 {~ms}^{-1}$, then at that instant, the magnitude of resultant acceleration will be

A particle of mass $m$ collides head-on with another stationary particle of mass $M$ such that the second particle starts moving and the first particle comes to rest after the collision. Which of the following conditions is valid if the coefficient of restriction is $e$?

Statement-I: A quick collision between two bodies is more violent than slow collision, even when initial and final velocities are identical.
Statement-II: The rate of change of momentum determines that the force is small or large.

KE of a body is increased by 44 % what is the percent increase in the momentum?

A long spring, when stretched by x cm has a potential energy U. On increasing the length of spring by stretching to nx cm, the potential energy stored in the spring will be

Two bodies of mass M and m are moving with same kinetic energy. If they are stopped by same retarding force, then

The quantity that is not conserved in an inelastic collision is

A person stands on a spring balance at the equator. By what percentage is the balance reading less than his true weight?

A block of mass $5 \mathrm{~kg}$ is moving along $x$-axis under the action of a variable force $F=10 x \mathrm{~N}$. The work done by the force in moving the block from $x=4 \mathrm{~m}$ to $x=6 \mathrm{~m}$ will be

A coin placed on a rotating turn table just slips if it is placed at a distance of 8 cm from the centre. If angular velocity of the turn table is doubled, it will just slip at a distance of

For motion under an external conservative force, which quantity is conserved?

Find out the power of an engine which can draw a train of ' 400 ' metric ton up the inclined plane of 1 in 98 at the rate $10 \mathrm{~ms}^{-1}$. The resistance due to friction acting on the train is ' 10 ' $\mathrm{N}$ per ton.

A body is falling freely under the action of gravity alone in vacuum. Which of the following quantities remain constant during the fall?

A uniform chain of length $L$ and mass $M$ is lying on a table and $\frac{1}{4}^{\text {th}}$ 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 back on the table

Assertion: The work done in moving a body over a closed loop is zero for every force in nature.
Reason: Work done depends on nature of force.

A force $\vec{F}=3 \hat{i}-2 \hat{j}+4 \hat{k}$ displaces a body from a point $A(8,-2,-3)$ to the point $B(-2,0,6)$. The work done is

Assertion: when a spring is elongated work done by spring is negative but when it compressed work done by spring is positive.
Reason: Work done by spring is path dependent.

Assertion: For an isolated system mechanical energy is conserved.
Reason: Kinetic frictional force is absent for isolated system.

A certain spring is found not to obey Hooke's law, it exerts a restoring force $F(x)=-\alpha x-\beta x^2$ if it is stretched or compressed, where $\alpha=48 \mathrm{~N} / \mathrm{m}$ and $\beta=24 \mathrm{~N} / \mathrm{m}^2.$ The mass of the spring is negligible. An object with mass $1 \mathrm{~kg}$ on a frictionless, horizontal surface is attached to the spring, pulled a distance $1 \mathrm{~m}$ to the right to stretch the spring and released. The speed of the object when it is $0.5 \mathrm{~m}$ to the right of the $x=0$ equilibrium position is

Work done by conservative forces acting on body is always equal to

A car is negotiating a curved road of radius $R$. The road is banked at an angle $\theta$. The coefficient of friction between the tyres of the car and the road is $\mu_s$. The minimum safe speed such that the car does not slip on this road is; (consider $\tan \theta < \mu_s$ )

A $500 \mathrm{~kg}$ car takes a round turn of radius $50 \mathrm{~m}$ with a velocity of $36 \mathrm{~km} \mathrm{~h}^{-1}$. The centripetal force is

Which of the following quantities measured from different inertial reference frames are same?

How much is the mass of a man if he has to do 2500 joule of work in climbing a tree $5 \mathrm{~m}$ tall ? $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$

A ball hits the floor and rebounds after inelastic collision. In this case

The closed line integral of force $\vec{F}$ taken along the closed curve is given by $\oint \vec{F} \cdot d \hat{l}$. If the force $\vec{F}$ is conservative, then the value of this integral is

The total energy of the universe is

The potential energy of a weight less spring compressed by a distance a is proportional to

Statement-I: When a body is rotated along a vertical circle with uniform speed then the sum of its kinetic energy and potential energy is constant at all positions
Statement-II: To make a body to move along a vertical circle, its critical speed at a point is independent of mass of body