Work-energy-power practice · Mixed difficulty

A body in equilibrium may not have

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

Assertion: For looping a vertical loop of radius, $r$ the minimum velocity at point should be $\sqrt{5 g r}$.

Reason: In this even the velocity at the highest point will be zero.

When two bodies stick after collision, the collision is known as

A ball is dropped from height 10 m. Ball is embedded in sand 1 m and stops, then

A chain of length $\text{L}$ and mass $\text{M}$ is held on a frictionless table with $\text{1/nth}$ of its length hanging over the edge. When the chain is released find the speed of chain while leaving the table is:

A stone of mass m is tied to a string of length l and rotated in a circle with a constant speed v. If the string is released, the stone flies

Toy cart tied to the end of an unstretched string of length a, when revolved moves in a horizontal circle of radius 2a with a time period T. Now the toy cart is speeded up until it moves in a horizontal circle of radius 3a with a period $T'$. If Hook’s law holds then

If the kinetic energy of a body is 5 times its momentum its velocity is

A body of mass m having an initial velocity v, makes head on collision with a stationary body of mass M. After the collision, the body of mass m comes to rest and only the body having mass M moves. This will happen only when

In which type of collision, the momentum of system is conserved?

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 heavy particle is tied to the end $A$ of a string of length $1.6 \mathrm{~m}$. Its other end $O$ is fixed. It revolves as a conical pendulum with the string making $60^{\circ}$ with the vertical. Then:

Statement I: Both stretched and compressed springs possess potential energy.

Statement II: Work done against restoring force is stored as potential energy.

Assertion(A): A spring of force constant $k$ is cut into two pieces having lengths in the ratio $1: 2$. The force constant of series combination of the two parts is $3 k / 2$.

Reason(R): The spring connected in series are represented by $k=k_1+k_2$.

When a belt moves horizontally at a constant speed of $1.5\mathrm{ }m{s^{ - 1}}$ , gravel is falling on it at $5\mathrm{ }kg{s^{ - 1}}$. Then the extra power needed to drive the belt is

A spring of constant $5 \times {10^3}\,N/m$ is stretched initially by 5 cm from the constracted position. The work required to stretch further by another 5 cm is

A ball is thrown with a velocity of 6m/s vertically downwards from a height H=3.2m above a horizontal floor. If it rebounds back to same height then coefficient of restitution e is $\left[ {g = 10\mathrm{ }m/{s^2}} \right]$

A man pushes a wall and falls to displace it. He does

The position x of a particle of mass 2 kg moving along straight line is given as $x = {\left( {t - 2} \right)^2}$, where t is in second and x is in metre. The work done by the force in first 2s is

A particle is moving in a circular path of radius a under the action of an attractive potential $U = - \frac{k}{{2{r^2}}}$ Its total energy is

When a body moves in a circular path, no work is done by the force since,

A car is moving on a circular horizontal track of radius 20m with a constant speed of 20 m/s. A simple pendulum of length 50cm hangs from the roof of the car. The angle made by the string of pendulum with the vertical is

In stable equilibrium position, a body has

A person of mass 50 kg carrying a load of 20 kg walks up a stair case. If the width and height of each step are 0.25 m and 0.2 m respectively, the work done by the man in walking up 20 steps is

Two spheres whose radii are in the ratio 1:2 are moving with velocities in the ratio 3:4. If their densities are in the ratio 3:2, the ratio of their kinetic energies is,

A ball is bouncing down a flight of stairs. The coefficient of restitution is $e$. The height of each step is $d$ and the ball descends one step each bounce. After each bounce it rebounds to a height $h$ above the next lower step. The height is large enough compared with the width of step so that the impacts are effectively headon. Find the relationship between $h$ and $d$.

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 projectile is fired at $30^{\circ}$ with momentum p. Neglecting friction, the change in kinetic energy when it returns to the ground will be

For a particle moving in vertical circle, the total energy at different positions along the path