Work-energy-power practice · Mixed difficulty

Force on a particle moving in straight line is given by $\vec{F}=6 t^2 \hat{i}-3 t \hat{j}$ and velocity is $\vec{v}=3 t^2 \hat{i}+6 t \hat{j}$. Find power at $t=2$.

Two springs with spring constants $k_1=1200 \mathrm{~N} / \mathrm{m}$ and $k_2=500 \mathrm{~N} / \mathrm{m}$ are stretched by the same force. The ratio of potential energy in the springs will be

A steel sphere of mass 100 gm moving with a velocity of 4 m/s collides with a dust particle elastically moving in the same direction with a velocity of 1 m/s. The velocity of the dust particle after the collision is

A ball $A$ moving with certain velocity along positive $x$-axis collides with a stationary ball $B$. After collision their directions of motion make angles $\alpha$ and $\beta$ with the $x$-axis. The possible values of $\alpha$ and $\beta$ are

A long spring when stretched by 2 cm its potential energy is $U$. If the same spring is stretched by 8 cm, then the potential energy of the spring is

Assertion(A): The relative velocity of the two particles in head on elastic collision is unchanged both in magnitude and direction.

Reason(R): The relative velocity is unchanged in magnitude but gets reversed in direction.

Assertion: Water at the foot of the water fall is always at different temperature from that at the top.
Reason: The potential energy of water at the top is converted into heat energy during falling.

A force $\overrightarrow F = (\hat i + 2\hat j + 3\hat k)N$ displaces a particle from position $\overrightarrow {{r_1}} = (\hat i + \hat j + \hat k)m$ to position $\overrightarrow {{r_2}} = (\hat j + \hat k)m$. The work done by the force in doing so is

Statement-I: Work done by spring force on a block connected to the spring may be positive or negative.
Statement-II: Spring force is both pushing and pulling.

Statement-1: A body can have energy without having momentum and vice versa.
Statement-2: The body having momentum must necessarily have kinetic energy.

A body having weight $0.4 \mathrm{~kg}$ is whirled in a vertical circle with a string making 2 revolutions/second. Given that the radius of this circle is 1.2 $\mathrm{m}$. Find out the tension

(a) At the top of the circle

(b) At the lowermost point of the circle.

Given : $\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$ and $\pi=3.14$.

Assertion (A): Graph between potential energy of a spring versus the extension or compression of the spring is parabola
Reason (R): Potential energy of a stretched or compressed spring proportional to square of extension or compression

Statement I Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement II Principle of conservation of momentum holds true for all kinds of collisions.

Assertion: If a body moving in a circular path has constant speed, then there is no force acting on it.
Reason: The direction of the velocity vector of a body moving in a circular path is changing.

Statement I: In an elastic collision of two billiards balls, the kinetic energy is not conserved during the short interval of time of collision between the balls.

Statement II: Energy spent against friction does not follow the law of conservation of energy.

A body projected vertically from the earth reaches a height equal to earth’s radius before returning to the earth. The power exerted by the gravitational force is greatest

You lift a heavy book from the floor of the room and keep it in the book–shelf having a height 2 m. In this process you take 5 seconds. The work done by you will depend upon

Which of the following quantity is conserved in an elastic collision between two bodies during the collision?

This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements. If two springs $S_1$ and $S_2$ of the force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$.
Statement-I: If stretched by the same amount, work done on $S_1$, will be more than that of $S_2$
Statement-II : $k_1 < k_2$

The force on a particle as the function of displacement ${x}$ (in ${x} /$ direction) is given by
${F}=10+0.5 {x}$

The work done corresponding to displacement of particle from ${x}=0$ to ${x}=2$ unit is

Assertion: Quick collisions are more violent than slow collisions.
Reason: Quick collision are inelastic in nature.

When a rubber band is stretched by a distance $x$, it exerts a restoring force of magnitude $F = ax + b{x^2},$ where $a$ and $b$ are constants. The work done in stretching the unstretched rubber-band by $L$ is

A particle of mass $m$ moves on a straight line with its velocity varying with the distance travelled according to the equation $v=\alpha x^{3 / 2}$, where $\alpha$ is a constant. The total work done by all the forces during a displacement from $x=0$ to $x=b$ is;

Assertion (A)In an elastic collision between two bides, the relative speed of the bodies after collision is equal to the relative speed before the collision.

Reason (R) In elastic collision, the linear momentum of the system is conserved.

A ball of mass m moves with speed v and strikes a wall having infinite mass and it returns with same speed then the work done by the ball on the wall is

Assertion: A car moving on a horizontal road may be thrown out of the road in taking a turn due to lack of proper centripetal force.
Reason: If a particle moves in a circle, describing equal angles in equal intervals of time. Then the velocity vector changes its magnitude.

A bullet of mass 10 Gm strikes a target at 400 m/s velocity and loses half of its initial velocity. The loss of kinetic energy in joules is

A car travelling at a speed of $30 {~km} / {hour}$ is brought to a halt in $8 {~m}$ by applying brakes. If the same car is travelling at $60 {~km} / {hour}$, it can be brought to a halt with the same braking force in

The bob of a simple pendulum having length $2 \mathrm{~m}$, is displaced from mean position to an angular position $\theta$ from vertical. If it is released, then velocity of bob at lowest position will be

Assertion: Kinetic energy of a body becomes four times, when its linear momentum is doubled.
Reason: This is because, $\mathrm{K.E.}=p^2 / 2 \mathrm{~m}$.