Work-energy-power practice · Mixed difficulty

This question has Statement I and Statement II. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement I A point particle of mass $m$ moving with speed $v$ collides with stationary point particle of mass $M$ . If the maximum energy loss possible is given as $f\left( {\frac{1}{2}m{v^2}} \right),\,$ then $f = \left( {\frac{m}{{M + m}}} \right)$

Statement II Maximum energy loss occurs when the particles get stuck together as a result of the collision.

A particle is moving in a horizontal circle with constant speed. It has constant

A body constrained to move is Z direction is subjected to a force given by $\overline F = \left( {4i - 12j + 6k} \right)N$ What is the work done by the force is moving the body through a distance of 5 cm along Z-axis

Consider the following statements A and B identify the correct choice in the given answers
A) In a one-dimensional perfectly elastic collision between two moving bodies of equal masses, the bodies exchange their velocities after the collision
B) If a lighter body at rest suffers head-on and perfectly elastic collision with a very heavy body moving with a certain velocity, after the collision both travel with same velocity

Statement-I: The normal force on a body by the floor is not a conservative force
Statement-II: The normal force does no work at all. Hence it will not store energy in the system.

The area of the acceleration-displacement curve of a body gives

Consider the following statements. A and B and identify the correct answer given below. I. Body initially at rest is acted upon by a constant force. The rate of change of its kinetic energy varies linearly with time. II. When a body is at rest, it must be in equilibrium.

The coefficient of restitution $e$ for a perfectly elastic collision is

A particle is moving on a circular path with constant speed, then its acceleration will be

A bullet of mass 25 g moving with velocity of 400 m/s enters into a wooden block and comes out of it with a velocity of 100 m/s. Find the work done by the bullet while passing through the wooden block.

A steel ball of mass 5 g is thrown downward with velocity $10\;\mathrm{m}{\mathrm{s}^{ - 1}}$ from height 19.5 m. It penetrates sand by 50 cm. The change in mechanical energy will be $\left( {\mathrm{g} = 10\,\,\mathrm{m}{\mathrm{s}^{ - 2}}} \right)$

Two bodies A and B of definite shape (dimensions of bodies are not ignored). A is moving with speed of 10 $\mathrm{m}{\mathrm{s}^{ - 1}}$ and B is in rest, collide elastically. The

When a body moves with some friction on a surface

A 1 kg block moving with velocity of 4 m/s collides with stationary 2 kg block. The lighter block comes to rest after collision. The loss of kinetic energy of the system is

A man, by working a hand pump fixed to a well, pumps out $10\mathrm{\;}{\mathrm{m}^3}$ water in 1 s. If the water in the well is 10 m below the ground level, then the work done by the man is $\left( {\mathrm{g} = 10\mathrm{m}{\mathrm{s}^{ - 2}}} \right)$

In a circular motion of a particle, the tangential acceleration of the particle is given by $a_t=9 \mathrm{~m} / \mathrm{s}^2$. The radius of the circle is $4 \mathrm{~m}$. The particle was initially at rest. Time after which total acceleration of the particle makes an angle of $45^{\circ}$ with the radial acceleration is:

Two observers are situated in different inertial reference frames. Then

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U\left( x \right)\frac{a}{{{x^{12}}}}\; - \frac{b}{{{x^6}}}$ ,where a and b are constants and x is the distance between the atoms , If the dissociation energy of the molecule is $D = \left[ {U\left( {x = \infty } \right) - {U_{\mathrm{at\,\,equilibrium}}}} \right],D$ is

If the linear momentum is increased by $50\%$, then kinetic energy will be increased by

When a particle is moving in a vertical circle,

The potential energy of a particle of mass 5 kg moving in the x-y plane is given by $U = \left( { - 7x + 24y} \right)J$, x and y being in metre. If the particle starts from rest from origin then speed of particle at t=2 s is

The decrease in the potential energy of a ball of mass 20 kg which falls from a height of 50 cm is

In the elastic collision of objects

If the coefficient of restitution is 0.5, what is the percentage loss of energy on each rebounding of a ball dropped from a height?

If $\bar F = \left( {55i + 16j - 4k} \right)N$ and $V = \left( {3i - 5j + 6k} \right)\,m/s$. Then instantaneous power is

Assertion: In elastic collision, kinetic energy is conserved.
Reason: Energy is always conserved.

A particle moves in a circular orbit of radius r under a central attractive force $F = - \frac{k}{r}$, k is constant. The time period of its motion is proportional to

The ratio of angular speeds of the minutes hand and the hours hand of a watch is

The work done by a force $\overrightarrow F = - \left( {4{x^3}\hat i} \right)$ N is displacing a particle from x=3m to x=-1m is

An object is being weighed on a spring balance moving around a curve of radius 100 m at a speed $7\;\mathrm{m}{\mathrm{s}^{ - 1}}$ The object has a weight of 60 kg-wt. The reading registered on the spring balance would be