Work-energy-power practice · Medium

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 force of 1200 N acting on a stone by means of rope slides the stone through a distance of 10 m in a direction inclined at ${60^0}$ to the force. The work done by the force is [Joules].

The power of a pump, which can pump 200 kg of water to a height of 200 m in 10 sec is ( g=$10m/{s^2}$)

In an inelastic collision which of the following does not remain conserved?

Mud thrown on a wall and sticking to it is an example for:

A force moves a block of mass $4 \mathrm{~kg}$ on horizontal smooth surface such that the position $x$ of the block as a function of time $t$ is given as $x=t^3$. Here $x$ is in metre and $t$ is in second. Work done by the force in first three second is

A particle of mass $m$ moves on a straight line with its velocity increasing with distance according to the equation $\mathrm{v}=\alpha \sqrt{\mathrm{x}}$, where $\alpha$ is a constant. The total work done by all the forces applied on the particle during its displacement from $\mathrm{x}=0$ to $\mathrm{x}=\mathrm{d}$, will be:

A body of mass $2 \mathrm{~kg}$ moving under a force has relation between displacement $x$ and time $t$ as $x=\frac{t^3}{3}$ where $x$ is in metre and $t$ is in sec. The work done by the body in first two second will be

A body dropped from a height $H$ reaches the ground with a speed of $1.2 \sqrt{g H}$. Calculate the work done by air-friction.

An object of mass $m$ slides down a hill of arbitrary shape and after travelling a certain horizontal path stops because of friction. The total vertical height descended is $h$. The friction coefficient is different for different segments for the entire path but is independent of the velocity and direction of motion. The work that a tangential force must perform to return the object to its initial position along the same path is

Which of the following statements is correct?

Roads are banked on curves so that

A bullet fired from a gun with a velocity of ${10^4}\mathrm{\;m}{\mathrm{s}^{ - 1}}$ goes through a bag full of straw. If the bullet loses half of its kinetic energy in the bag, its velocity when it comes out of the bag will be

Two particles are seen to collide and move jointly together after the collision. During such a collision, for the total system,

When work done on a particle is positive
a) K.E remains constant
b) Momentum increases
c) K.E increases
d) K.E decreases

The slope of kinetic energy and displacement curve for a particle in motion will be

A particle moves along x-axis from x=1m to x=3m under the effect of the force $F = 3{x^2} - 2x + 5\mathrm{ }N$ work done in process is

Two spherical bodies of the same mass M are moving with velocities ${v_1}\,and\,{v_2}$ .These collide perfectly inelastically , then the loss in kinetic energy is

The potential energy of $1kg$ particle free to move along the $x - axis$ is given by $U\,(x) = \left[ {\frac{{{x^4}}}{4} - \frac{{{x^2}}}{2}} \right]J$. The total mechanical energy of the particle is $2J$. What is the maximum speed $\left( {in\,\,m{s^{ - 1}}} \right)$ of the particle?

A body of mass ${m}$ attached to a thread is revolved along a vertical circle of radius $r$. If its velocity at the topmost point of the circle is $v$, the tension of the thread at the instant will be :

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

Assertion (A): Collision between two particles is not necessarly associated with physical contact between them
Reason(R): Only in physical contact, momentum transfer takes place

If a particle of mass $m_1$ approaches another particle of mass $m_2$, initially at rest, with speed $v_v$, the speed of the $\mathrm{cm}$ of the system is $v_{\mathrm{cm}}=\frac{m_1 v_1}{m_1+m_2}$ before collision takes place. If the collision is elastic, the speed of the $\mathrm{cm}$ of the system after the collision is

Which of the following forces does not act on a body moving in uniform circular motion?

A ball is spun with angular acceleration $\alpha = 6{t^2} - 2t$, where $t$ is in second and $\alpha$ is in $rad{s^{ - 2}}$. At $t = 0$, the ball has angular velocity of $10\,rad{s^{ - 1}}$ and angular position of 4 rad. The most appropriate expression for the angular position of the ball is:

A solid sphere of mass $2 \mathrm{~kg}$ is rolling on a frictionless horizontal surface with velocity 6 $\mathrm{m} / \mathrm{s}$. It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring $=36 \mathrm{~N} / \mathrm{m}$).

A body is acted upon by a constant force directed towards a fixed point. The magnitude of the force varies inversely as the square of the distance from the fixed point. What is the nature of the path?

Assertion(A): If work done by conservative force is negative, then potential energy associated with that force should increase.

Reason(R): This is according to the relation, $\Delta U=-W$. Here, $\Delta U$ is change in potential energy and $W$ is work done by conservative force.

A ball hits a floor and rebounds after an inelastic collision. In this case,
a) Total energy of the ball and the earth remains the same
b) Total momentum of the ball and the earth is conserved
c) Momentum of the ball just after the collision is same as that just before the collision
d) Mechanical energy of the ball remains the same during the collision

A projectile is fired from the top of a $40 \mathrm{~m}$ high cliff with an initial speed of $50 \mathrm{~m} / \mathrm{s}$ at an unknown angle. Find its speed when it hits the ground.