Work-energy-power practice · Mixed difficulty

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.

A particle of mass $M$ is moving in a circle of fixed radius $R$ in such a way that its centripetal acceleration at time $t$ is given by $n^2 R t^2$ where $n$ is a constant. The power delivered to the particle by the force acting on it, is

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

Assertion: There is no loss in energy in elastic collision
Reason: Linear momentum is conserved in elastic collision

A motor boat is going in a river with velocity $\vec V = 4\hat i - 2\hat j + \hat k\,m{s^{ - 1}}$. If the resisting force due to stream is $\overrightarrow F = \left( {5\hat i - 10\hat j + 6\hat k} \right)N$, then the power of motor boat is

A body of mass 0.1 kg moving with a velocity of 10 m/s hits a spring (fixed at the other end) of force constant 1000 N/m and comes to rest after compressing the spring. The compression of the spring is

A body of mass $1 \,{gm}$ is released down an inclined plane describes a circle of radius $10 {~cm}$ in the vertical plane on reaching the bottom. The minimum height of that inclined plane is

A block of mass $1.0 \mathrm{~kg}$ moving on a horizontal surface with speed $2 \mathrm{~m} / \mathrm{s}$ enters a rough surface. The retarding force $\left(F_r\right)$ on the block is given by

$F_r=\left\{\begin{array}{l} -\frac{k}{x} ; 10 \mathrm{~m} < x < 100 \mathrm{~m} \\ 0 ; x < 10 \mathrm{~m} \text { and } x > 100 \mathrm{~m} \end{array}\right.$

where $k=0.5 \mathrm{~J}$. The kinetic energy of the block at $x=100 \mathrm{~m}$ is

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

Work done by the gravitational force on a body of mass &lsquo;m&rsquo; moving on a smooth horizontal surface through a distance &lsquo;s&rsquo; is.

Kinetic energy of any moving particle is

The kinetic energy of particle continuously increase with time
a. The resultant force on the particle must parallel to velocity at all instants
b. The resultant force on the particle at an angle less than $90^{\circ}$ all the time
c. Its height above the ground level continuously decrease
d. The magnitude of its linear momentum is increasing continuously

A stone of mass 1 kg tied to a light inextensible string of length $L = \frac{{10}}{3}$ is whirling in a circular path of radius L in vertical plane. If the ratio of the maximum tension to the minimum tension in the string is 4. What is the speed of stone at the highest point of the circle? (Taking $\mathrm{g} = 10\mathrm{m}{\mathrm{s}^{ - 2}}$)

A stream of particles $\alpha$-particles encounters a stationary unknown nucleus in a cloud chamber. After a collision, the two nuclei are scattered in mutually perpendicular directions. If some kinetic energy is lost in the collision, the unknown nucleus must be

Statement I: The maximum speed at which a car can turn on level curve of radius $40 \mathrm{~m}$, is $11 \mathrm{~m} / \mathrm{s} ; \mu=0.3$.

Statement II: $v=\sqrt{\mu \mathrm{Rg}} \Rightarrow \mu=\frac{\mathrm{v}^2}{\mathrm{Rg}}=\frac{11 \times 11}{40 \times 10}=0.3$.

What average power is generated by a $90.0 \mathrm{~kg}$ mountain climber who climbs a summit of height $600 \mathrm{~m}$ in $90.0 \mathrm{~min}$ ?

When a body falls freely under gravity, then the work done by the gravity is:

A stone is moved in a horizontal circle of radius $4 \mathrm{~m}$ by means of a string at the height of $20 \mathrm{~m}$ above the ground. The string breaks and the particles fliesoff horizontally, striking the ground $10 \mathrm{~m}$ away. The centripetal acceleration during circular motion is given by

Assertion (A): Collision between two fundamental particles is elastic
Reason (R): Fundamental particles lose their shape in collision

The velocity vector of a sphere after it hits a vertical wall which is parallel to $\hat{j}$ is $(-\hat{i}+3 \hat{j})$ on a smooth horizontal surface. The coefficient of restitution between ball and wall is (1/2). Find the velocity vector of sphere immediately before collision.

You lift a suitcase from the floor and keep it on table. The work done by you on the suitcase does not depend on
a. The path taken by the suitcase
b. The time taken by you in doing so
c. The weight of the suitcase
d. Your weight

A boy of mass 1 kg moves from point A(2m,3m,4m) to B(3m,2m,5m). During motion of body, a force $\mathbf{\vec F} = \left( {2\mathrm{N}} \right)\hat i - \left( {4\mathrm{N}} \right)\hat j$ acts on it. The work done by the force on the particle displacement is

By burning $1 \mathrm{~g}$ of coal, the energy produced is $2 \mathrm{kcal}$. Then for $1 \mathrm{kWh}$, the quantity of coal so required will be nearly

Assertion: No work is done by a force on an object when the point of application of the force does not move.
Reason: A small block of mass $m$ is kept on a rough inclined surface of inclination $a$ fixed in an elevator. The elevator goes up with a uniform velocity $u$ and the block does not slide on the wedge. Then the work done by the force of friction on the block in time $t$ will be $mgut \sin ^2 \alpha$.

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

Two balls of same mass are projected one vertically upwards and the other at angle $60^{\circ}$ with the vertical. The ratio of their potential energy at the highest point is

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 $k=k_1+k_2$.

A sphere $P$ of mass $m$ and velocity $\overrightarrow{v_i}$ undergoes an oblique and perfectly elastic collision with an identical sphere $Q$ initially at rest. The angle $\theta$ between the velocities of the spheres after the collision shall be

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

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