Work-energy-power practice · Mixed difficulty

Potential energy is defined

Two particles A and B move with constant velocities $\overrightarrow {{v_1}} \,\,\mathrm{and}\,\,\overrightarrow {{v_2}}$. At the initial moment their position vectors $\overrightarrow {{r_1}} \,\,\mathrm{and}\,\,\overrightarrow {{r_2}}$
respectively. The condition for particles A and B for their collision is:

In elastic collision, 100% energy transfer takes place when

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.

Work done by a conservative force on a system is equal to

Assertion (A): In circular motion work done by all the forces acting on the body is zero.

Reason (R) : Centripetal force and velocity are mutually perpendicular.

Assertion: Centripetal force does no work.

Reason: Force and displacement are perpendicular to each other.

A 2.0 kg block is dropped from a height of 40 cm onto a spring of spring constant $k = 1960\;\mathrm{N}{\mathrm{m}^{ - 1}}$ . Find the maximum distance the spring is compressed

A rock of mass m is dropped to the ground from a height h. A second rock with mass 2m is dropped from the same height. When second rock strikes the ground, what is its kinetic energy?

From a water fall, water is pouring down at the rate of 90 kg/s on the blades of a turbine. If the height of the fall is 90 m the power delivered to the turbine is approximately equal to

A free body of mass 8 kg is travelling at 2 meter per second in a straight line. At a certain instant, the body splits into two equal parts due to internal explosion which releases 16 joules of energy. Neither part leaves the original line of motion finally, then

The potential energy function along the positive $x$-axis is given by $U(x)=-a x+\frac{b}{x}, a$ and $b$ are constants. If it is known that the system has only one stable equilibrium configuration, the possible values of $a$ and $b$ are

A body of mass 10 kg is acted upon by two forces each of magnitude 10 N making an angle of ${60^0}$ with each other. Find the net acceleration of the body

Assertion (A) : When water in a bucket is whirled fast overhead, the water does not fall out at the top of the circular path.

Reason (R) : The centripetal force in this position on water is more than the weight of water.

A ball of mass m moving the velocity V collides head on with another ball of the same mass at rest. If e is coefficient of restitution, their velocities after collision are

Two bodies of masses ${m_1}\,\,\mathrm{ and }\,\,{m_2}$ have same kinetic energy. The ratio of their momentum is

For motion under an external conservative force, which quantity is conserved?

When a 1.0 kg mass hangs attached to a spring of length 50 cm, the spring stretches by 2 cm. The mass is pulled down until the length of the spring becomes 60 cm. What is the amount of elastic energy stored in the spring in this condition, if $g = 10\;m/{s^2}$

The angular acceleration of a body, moving along the circumference of a circle, is

The potential energy of a particle of mass $1 \mathrm{~kg}$ is $U=10+(x-2)^2$. Here, $U$ is in joule and $x$ in metre on the positive $X$-axis. Particle travels upto $x=+6 \mathrm{~m}$. Choose the correct option.

The two moving particles collide and clump together on a smooth horizontal surface. The following statements are given below
a) Mechanical energy is conserved
b) Total energy is conserved
c) Work done by the system is positive
d) Work done by the system is negative
Choose the correct option.

A body of mass 6kg is under a force which cause displacement in it given by $S = \frac{{{t^2}}}{4}$ metres where t is time. The work done by the force in 2 seconds is

Identify the correct statements from the following:

A. Work done by a man in lifting a bucket out of a well by means of rope tied to the bucket is negative.

B. Work done by gravitational force in lifting a bucket out of a well by a rope tied to the bucket is negative.

C. Work done by friction on a body sliding down an inclined plane is positive.

D. Word done by an applied force on a body moving on a rough horizontal plane with uniform velocity is zero.

E. Work done by the air resistance on an oscillating pendulum is negative.

Choose the correct answer from the options given below:

Potential energy function along $x$-axis in a certain force field is given as $U(x)=\frac{x^4}{4}-2 x^3+\frac{11}{2} x^2-6 x$. For the given force field,

(i) the points of equilibrium are $x=1, x=2$ and $x=3$

(ii) the points $x=2$ is a point of unstable equilibrium

(iii) the points $x=1$ and $x=3$ are points of stable equilibrium

(iv) there exists no point of neutral equilibrium Which one of the following is the set of correct options?

Which of the following statements is FALSE for a particle moving in a circle with a constant angular speed?

The potential energy function associated with the force $\vec{F}=4 x y \hat{i}+2 x^2 \hat{j}$ is

A point of application of a force $\mathrm{\vec F} = 5\hat i - 4\hat j + 2\hat k$ is moved from $\overrightarrow {{\mathrm{r}_1}} = 2\hat i + 7\hat j + 4\hat k\,to\,\overrightarrow {{\mathrm{r}_2}} = 5\hat i + 2\hat j + 3\hat k$ the work done is

A body mass 9 kg is raised from a certain depth. By the time it is raised by 9m if its velocity is 2 m/s work done during this time is (take $g = 10\,m/{s^2}$)

The displacement x in metre of a particle of mass m kg moving in one dimension under the action of a force is related to the time t in second by the equation $t = \sqrt x + 3$, the work done by the force (in joule) in first six seconds is

A force of 5 N is applied on a 20 kg mass at rest. The work done in the third second is,