Work-energy-power practice · Mixed difficulty

The kinetic energy of a body decreases by 36%. The decrease in linear momentum is

For an isolated system in the absence of any dissipative effect
a) KE is conserved
b) PE is conserved
c) Energy is conserved
d) ME is conserved

A stone is whirled in a vertical plane. The stone generally has

A particle free to move along the x-axis has potential energy given by $U\left( x \right) = k\left[ {1 - \exp \left( { - {x^2}} \right)} \right]$ for $- \infty \le x \le + \infty$ where k is a positive constant of appropriate dimensions. Then

If the kinetic energy of a body increases by 125%, the percentage increase in its momentum is

A body is travelling in a circle at a constant speed. It

In a tug of war, the team that exerts a larger tangential force on the ground wins. Consider the period in which a team is dragging the opposite team by applying a larger tangential force on the ground. Which of the following works are negative?

Assertion (A): If the momentum of a body increases by $20 \%$, then its KE also increases by $20 \%$
Reason (R): The KE of a body is directly proportional to its momentum

Statement I: The centripetal force and the centrifugal force never cancel out.
Statement II: They do not act at the same time.

The displacement $x$ and time $t$ for a particle are related to each other as $t=\sqrt{x}+3$. What is work done in first six seconds of its motion?

A body of mass $10 \mathrm{~g}$ moving with velocity $5 \mathrm{~ms}^{-1}$ collides with another body of mass $15 \mathrm{~g}$ moving with $3 \mathrm{~ms}^{-1}$ in the same direction. After collision if they stick and move together, the loss of kinetic energy of the system is

A cricket ball is hit at ${30^0}$ with the horizontal with kinetric energy ${E_k}$. What is the kinetic energy at the highest point?

A body of mass 0.1 kg moving with a velocity of 10 m/s hits a spring (fixed at the other end) of force constant 1000 N/m and comes to rest after compressing the spring. The compression of the spring is

A train is moving with a uniform velocity of $\left( {2\hat i - \hat j + 4\hat k} \right)\,m{s^{ - 1}}$. If the force required to overcome friction is $\left( {\hat i - 3\hat j + 2\hat k} \right)N$, the power of the engine is [watts]

Assertion (A) : Velocity and acceleration of a particle in circular motion at some instant are: $\mathbf{v}=(2 \hat{\mathbf{i}}) \mathrm{ms}^{-1}$ and $\mathbf{a}=(-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}) \mathrm{ms}^{-2}$, then radius of circle is $2 \mathrm{~m}$.

Reason (R) : Speed of particle is decreasing at a rate of $1 \mathrm{~ms}^{-2}$.

Kinetic energy of a particle moving in a straight line varies with time $t$ as $K=4 t^2$. The force acting on the particle

A force of $\left( {3i + 4j + 5k} \right)N$act on a body and produced a displacement of $\left( {4i + 5j + 6k} \right)m.$ Then the amount of work done is

The potential energy of a system increases if work is done

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

Assertion(A): Force applied on a block moving in one dimension is producing a constant power, then the motion should be uniformly accelerated.

Reason(R): This constant power multiplied with time is equal to the change in kinetic energy.

When a spring is fixed at one end and a force is applied at the other end and as the applied force increases, deformation in the spring is

An object moves along a straight line path from P to Q under the action of a force $\left( {4\hat i - 3\hat j + 3\hat k} \right)$ N. If the coordinates of P and Q, in metres, are (3,3,-1) and (2,-1,4) respectively, then the work done by the force is

Two bodies $A$ and $B$ of same mass undergo completely inelastic one dimensional collision. The body $A$ moves with velocity $v_1$ while body $B$ is at rest before collision. The velocity of the system after collision is $v_2.$ The ratio $v_1: v_2$ is

A stone of mass 1 kg tied to a light inextensible string of length $L = \frac{{10}}{3}m$ is whirling in a circular path of radius L in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if g is taken to be $10m/{\sec ^2}\;,$ the speed of the stone at the highest point of the circle is

Three identical balls A,B and C are lying on a horizontal frictionless table as shown in figure. If ball A is imparted a velocity v towards B and C and the collisions are perfectly elastic, then finally

Given below are two statements: one is labelled as Assertion A and the other is labeled as Reason R.
Assertion A: Body $P$ having mass $M$ moving with speed $u\,$has head-on collision elastically with another body $Q$ having mass $m$ initially at rest. If $m < < M$, body $Q$ will have a maximum speed equal to $2u\,$ after collision.
Reason R: During elastic collision, the momentum and kinetic energy are both conserved.
In the Light of the above statements, choose the most appropriate answer from the options given below.

A mass of 50 kg is raised through a certain height by a machine whose efficiency is $90\%$, the energy is 5000 J. If the mass is now released, its KE on hitting the ground shall be

Assertion: The work done by the spring force in a cyclic process is zero.
Reason: Spring force is a conservative force.

A bob of mass $m$, suspended by a string of length $l_1$, 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 length $\mathrm{l}_2$, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio $\frac{\ell_1}{\ell_2}$ is

A motor can pump the water up to maximum height of 10m at the rate of $10\,kg\,{s^{ - 1}}$ . If efficiency of the motor is 0.8 then power of motor is