Work-energy-power practice · Medium

Power applied to a particle varies with time t as $P = 4{t^2} - 3t + 2\,watt$, where t is in second. Find the change in its kinetic energy between time t = 0 s and t= 2 s

Which of the following statement(s) is/are correct?

I. Spring force is a conservative force.

II. Potential energy is defined only for conservative forces.

Statement-I: If both the speed of a body and radius of its circular path are doubled, then centripetal force also gets doubled.
Statement-II: Centripetal force is directly proportional to both speed of a body and radius of circular path.

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.

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

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

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

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

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 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

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

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

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

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

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?