Work-energy-power practice · Medium

Keeping the angle of banking of the road constant, the maximum speed of the vehicles is to be increase by $10 \%$. The radius of curvature of the road will have to be changed from $20 {~m}$ to

A uniform force of 4 N acts on a body of mass 10 kg for a distance of 2.0 m. The kinetic energy acquired by the body is

Assertion: A body can have energy without having momentum.
Reason: A body can have momentum without having mechanical energy.

A force $F$ acting on a body depends on its displacement ${s}$ as $F \propto s^{-1 / 3}$. The power delivered by ${F}$ will depend on displacement as

Assertion: If ball is dropped from a higher altitude. There will be a greater value of impulse from ground during collision.
Reason: Gravity increases momentum of a ball.

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?

Statement I: Work done in moving a body in non-uniform circular motion is zero.

Statement II: The centripetal force always acts along the radius of the circle.

Two bodies of masses $m$ and $2 m$ are moving along positive $x$ and $y$ axes respectively with equal speeds of $4 {~m} / {s}$. They collide at origin and stick together. The final velocity of combined mass 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:

The ratio of angular speeds of the minutes hand and the hours hand of a watch is

A) When a ball hits a wall (stationary) it returns back with same velocity, if collision is elastic
B) A ball hits a bus moving towards it. If the collision is inelastic, they move together.
C) Inelastic collision arises due to loss in K.E during collision

A person holds a bucket of weight 60 N. He walks 7m along the horizontal path and then climbs up a vertical distance of 5 m. The work done by the man is

The potential energy of a body is given by

$U=40+6 x^2-7 x y+8 y^2+32 z$
where $U$ is in joule and $x, y, z$ in metre. Deduce the $x, y$ and $z$ components of the force (in newton) on the body when it is in position $(-2,0,+5)$

STATEMENT-1 : In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.

STATEMENT-2 : In an elastic collision, the linear momentum of the system is conserved.

A car when passes through a convex bridge exerts a force on it which is equal to

During "elastic collision"
a) There is no loss of kinetic energy
b) The bodies are perfectly elastic
c) Temporarily some of the kinetic energy is used to deform the bodies
d) After collision the bodies regain the original shape keeping the total energy constant

A ball is thrown up from the earth by a person and then caught by him on its return. When the ball falls towards the earth, the ratio of kinetic energies gained by the ball $\left(K_B\right)$ and the earth $\left(K_E\right)$ is

An elastic string of unstretched length L and force constant k is stretched by a small length $x$. It is further stretched by another small length y. The work done in the second stretching is

A girl throws a ball with initial velocity $v$ at an inclination of $45^{\circ}$. The ball strikes the smooth vertical wall at a horizontal distance $d$ from the girl and after rebounding returns to her hand. What is the coefficient of restitution between wall and the ball?

A ball of mass ${m_1}$ is a moving with velocity $v$. It collides head on elastically with a stationary ball of mass ${m_2}$. The velocity of ball becomes v/3 after collision. Then the value of the ratio $\frac{{{m_2}}}{{{m_1}}}$ is

Two perfoctly elastic balls of same mass $\mathrm{m}$ are moving with velocities $\mathrm{u}_1$ and $\mathrm{u}_2$. They collide head on elastically $\mathrm{n}$ times. The kinetic energy of the system finally is:

A 10 m long iron chain of linear mass density $0.8\mathrm{\;kg\;}{\mathrm{m}^{ - 1}}$ is hanging freely from a rigid support. If $\mathrm{g} = 10\mathrm{\;m}{\mathrm{s}^{ - 2}}$, then the power required to lift the chain upto the point of support in 10 s is

Which of the following option is not correct for inelastic collision:

If F is the force required to keep a train moving at a constant speed v,the power required is

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

I. If momentum of a body increases by $50 \%$, its kinetic energy will increase by $125 \%$.

II. Kinetic energy is proportional to square of velocity.

A heavy weight is suspended from a spring. A person raises the weight till the spring becomes slack. The work done by him is $W$. The energy stored in the stretched spring was $E$. What will be the gain in gravitational potential energy?

A stone tied to one end of rope and rotated in a circular motion. If the string suddenly breaks, then the stone travels

A Neutron's moving with a certain kinetic energy collide head on with an atom of mass number '$A$'. Find the fraction of kinetic energy retained by it

A block of mass $m$ moving with speed $v$ collides with another block of mass $2 {~m}$ at rest. The lighter block comes to rest after the collision. The coefficient of restitution is

A particle strikes elastically with another particle with velocity $\mathrm{V}$. After the collision, it moves with half the velocity in the same direction. Find the velocity of the second particle if it is initially at rest