Work-energy-power practice · Mixed difficulty

A body is tided with a string and is given a circular motion with velocity v in radius r. The magnitude of the acceleration

A metal ball hits a wall and does not rebound whereas a rubber ball of the same mass on hitting the wall rebounds with the same speed. It can be concluded that

The centripetal acceleration of a particle varies inversely with the square of the radius rof the circular path .The KE of this particle varies directly as

In a shotput event an athlete throws the shotput of mass $10 \mathrm{~kg}$ with an initial speed of $1 \mathrm{~m} \mathrm{s}^{-1}$ at $45^{\circ}$ from a height 1.5 m above ground. Assuming a irresistance to be negligible and acceleration due to gravity to be $10 \mathrm{~m} \mathrm{s}^{-2}$, the kinetic energy of the shotput when it just reaches the ground will be

The potential energy of an object of mass $m$ moving in $xy$ plane in a conservative field is given by ${U}={ax}+{by}$, where ${x}$ and ${y}$ are position coordinates of the object. Find magnitude of its acceleration:

Assertion: Centripetal acceleration is applied in the direction of the centre of rotation of an object during uniform circular motion.
Reason: Centripetal acceleration is a constant vector.

A porter with a suitcase of mass $20 \mathrm{~kg}$ on his head moves up a staircase upto a height of $4 \mathrm{~m}$. The amounts of work done by the upward lifting force relative to him and relative to a person on the ground respectively, are

A police officer fires a bullet of mass $50 \,{gm}$ with speed $400 {~m} / {s}$ on soft plywood of thickness $2 {~cm}$. The bullet emerges with only $25 \%$ of it's kinetic energy. What is the emergent speed of the bullet?

Two students are sitting face to face, at two ends of a long compartment of a train, running at a constant acceleration. They toss a ball to each other, with the same muzzle velocity and at the same inclination to the vertical.
Statement-1: The time intervals for the free fall in either direction are equal.
Statement-2: In the frame of compartment velocity is changing but the vertical velocity remains unaffected by the horizontal acceleration of the cart.

A force of 5 N moves the particle through a distance of 10 m. If 25 J of work is performed, then the angle between the force and the direction of motion 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

Two identical bodies are executing uniform circular motion in the paths of radii ${r_1}$ and ${r_2}$ respectively. If both the bodies complete one revolution in the same time interval, then the ratio of their angular speeds is

Assertion: A light body and a heavy body have same momentum. Then they also have same kinetic energy.
Reason: Kinetic energy does not depend on mass of the body.

A body of mass $1 \mathrm{~kg}$ is moving in a vertical circular path of radius $1 \mathrm{~m}$. The difference between the kinetic energies at its highest and lowest position is

A meter stick of mass $400 \mathrm{~g}$ lying horizontally is pivoted at one end and displaced through an angle $60^{\circ}$. The increase in its potential energy is

Identify the wrong statement

A dam is situated at a height of 550 m above sea level and supplies water to a power house which is at a height of 50 m above sea level. 2000 kg of water passes through the turbines per second. What would be the maximum electrical power output of the power house if the whole system were 80% efficient?

In uniform circular motion, the velocity vector and acceleration vector are

If momentum of a body increases by $30 \%$ then percentage increase in its $KE$ will be

Two balls of masses 2g and 6g are moving with KE in the ratio of $3:1$. What is the ratio of their linear momenta?

A hollow sphere has radius 6.4 m. minimum velocity required by a motor cyclist at bottom to complete the circle will be [in m/s]

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m, 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies $3.8 \times {10^7}\,J$ of energy per kg which is converted to mechanical energy with a 20% of efficiency rate. (Take, $g = 9.8\,m{s^{ - 2}}$)

The vessels $A$ and $B$ of equal volume and weight are immersed in water to depth $h$. The vessel $A$ has an opening at the bottom through which water can enter. If the work done in immersing $A$ and $B$ are $W_A$ and $W_B$ respectively, then

A stone of mass 1 kg tied to the end of a string of length 1 m, is whirled in a horizontal circle with a uniform angular velocity 2 $\mathrm{rad}{\mathrm{s}^{ - 1}}$. The tension of the string is (in newton)

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

When force and displacement are in the same direction, the kinetic energy of the body:

A ball is thrown vertically upwards with a velocity of $20 \mathrm{~m} / \mathrm{s}$. At what height, will its kinetic energy be half its original value?

A body moves along a path $\mathrm{PQR}$ in horizontal plane from $\mathrm{P}$ to $\mathrm{R}$. When the particle is at $\mathrm{Q}$, its speed is decreasing. The acceleration of the particle at $\mathrm{Q}$ is best represented by the vector.(A, B, C and D are vectors)

A certain body of mass $M$ moves under the action of a conservative force with potential energy $U$ given by $U=\frac{K x}{x^2+a^2}(x \rightarrow$ distance, $a \rightarrow$ amplitude$)$ In this equation the units of ${K}$ will be equal to that of:

A force acts on a $3 \mathrm{~g}$ particle in such a way that position of particle as a function of time is given by $x=3 t-4 t^2+t^3$, where $x$ is in metre and $t$ is in sec. The work done during first $4 \mathrm{~s}$ is