Work-energy-power practice · Mixed difficulty

A shell, in flight explodes into four unequal parts which of the following is conserved.

A ball moving with a velocity $\bar{u}_1$ collides elastically with another ball of equal mass, in a onedimensional collision. Which of the following is not possible?

A particle moves from a point $\left( { - 3i + 5j} \right)$ to $\left( {6j + 4k} \right)$ when a force of $\left( {6i + 4j} \right)N$ is applied. How much work has been done by the force

A man is supported on a frictionless horizontal surface. It is attached to a string and rotates about a fixed centre at an angular velocity $\omega$. The tension in the string if F. If the length of string and angular velocity are doubled, the tension is string is now

Assertion: Work done by the force or against the force does not depend on path, then force is called conservative force.
Reason: All central forces which follows the inverse square law are conservative forces.

Assertion: Collision between two billiard's ball is inelastic
Reason: Momentum remains conserve during the collision

A ball is falling from a height of $2 \mathrm{~m}$ rebounds to a height of $1.5 \mathrm{~m}$ after hitting the ground. Then the percentage of energy lost is:

The potential energy function associated with the force $\vec{F}=4 x y \hat{i}+2 x^2 \hat{j}$ is

A body is moving horizontally at a height of $60 \mathrm{~m}$ has its P.E equal to K.E. Then velocity of that body is $\left(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$

The speed ${v}$ reached by a car of mass ${m}$ driven with constant power ${P}$ is given by

The length of an elastic string is $x$ when the tension is $5 \mathrm{~N}$. Its length is $y$ when the tension is $7 \mathrm{~N}$. What will be its length, when the tension is $9 \mathrm{~N}$?

A $5 \mathrm{~kg}$ object collides with a stationary $5 \mathrm{~kg}$ object and after collision, they stick together and move forward with velocity $6 \mathrm{~m} \mathrm{s}^{-1}$. What is the velocity with which the $10 \mathrm{~kg}$ object hits the second one ?

The centripetal force required by a 900 kg car that takes a turn of radius 40 m at a speed of 35 kmph is

The maximum speed of a car on a road turn of radius 30 m; if the coefficient of friction between the tyres and the road is 0.4; will be

A ball falls from a height of $16 {~m}$ on a floor and rebounds to a height of $4 {~m}$. The coefficient of restitution for collision is :-

Assertion (A): $n$ small balls each of mass '$m$' colliding elastically each second on a surface with a velocity $u$. The force experienced by the surface is $2 \mathrm{nmu}$.
Reason (R): In elastic collision, the ball rebounds with the same velocity

Angle between position vector and acceleration vector of a particle in non-uniform circular motion (centre of circle is taken as origin) may be

A force given by the relation $\text{F}=8 \text{t}$ acts on a body of mass $2 \mathrm{~kg}$ initially at rest. The work done by this force on the body during first $2 \mathrm{~s}$ of its motion is:

A particle is moving on a circular path of $10 \mathrm{~m}$ radius. At any instant of time, its speed is $5 \mathrm{~ms}^{-1}$ and the speed is increasing at a rate of $2 \mathrm{~ms}^{-2}$. At this instant, the magnitude of the net acceleration will be

If a particle is compelled to move on a given smooth plane curve under the action of given forces in the plane $\mathbf{\vec F} = x\hat i + y\hat j$ , then

A man is standing at a spring platform. Reading of spring balance is 60 kg wt. If man jumps outside platform, then reading of spring balance

A particle of mass ${m}$ is moving along the ${x}$ - axis under the potential $V(x)=\frac{k x^2}{2}+\frac{\lambda}{x^{\prime}}$ where ${k}$ and ${x}^{\prime}$ are positive constants of appropriate dimensions. The particle is slightly displaced from its equilibrium position. The particle oscillates with the angular frequency $({w})$ given by

Power applied to a particle varies with time as $P = \left( {3{t^2} - 2t + 1} \right)$ watt, where t is in second. Find the change in its kinetic energy between t=2 s and t=4 s

Assertion: A truck and a car moving with the same kinetic energy are brought to rest by the application of breaks which provide equal retarding forces. Both come to rest in equal distance.
Reason: It is possible that the speed of a body is zero but velocity is not zero.

In a circular motion of a body, which amongst the following relation between tangential acceleration and linear velocity is correct?

A body of mass $2 \mathrm{~kg}$ is projected vertically upwards with velocity $20 \mathrm{~m} / \mathrm{s}$. If the body rises to a height of $15 \mathrm{~m}$, the work done by air drag is $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$

Assertion (A): Work done by the gravitational force is zero, in closed path
Reason (R): Gravitational force is a conservative force

A particle is moving in a conservative force field from point $A$ to point $B . U_A$ and $U_B$ are the potential energies of the particle at points $A$ and $B$; and $W_C$ is the work done by conservative forces in the process of taking the particle from $A$ and $B$. Which of the following is true?

Assertion: The power of a pump which raises 100 kg of water in 10 sec to a height of 100 m is 10 KW.
Reason: The practical unit of power is horse power.

Three identical cars $A, B$ and $C$ are moving at the same speed on three bridges. The car $A$ goes on a plane bridge $B$ on a bridge convex upwards and $C$ goes on a bridge concave upwards. Let $F_A, F_B$ and $F_C$ be the normal forces exerted by the cars on the bridges when they are at the middle of the bridges. Then