Work-energy-power practice · Medium

A cricket ball is hit at ${30^0}$ with the horizontal with kinetric energy ${E_k}$. What is the kinetic energy at the highest point?

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

Assertion (A) : Velocity and acceleration of a particle in circular motion at some instant are: $\mathbf{v}=(2 \hat{\mathbf{i}}) \mathrm{ms}^{-1}$ and $\mathbf{a}=(-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}) \mathrm{ms}^{-2}$, then radius of circle is $2 \mathrm{~m}$.

Reason (R) : Speed of particle is decreasing at a rate of $1 \mathrm{~ms}^{-2}$.

Kinetic energy of a particle moving in a straight line varies with time $t$ as $K=4 t^2$. The force acting on the particle

The potential energy of a system increases if work is done

The potential energy of a weight less spring compressed by a distance a is proportional to

Assertion(A): Force applied on a block moving in one dimension is producing a constant power, then the motion should be uniformly accelerated.

Reason(R): This constant power multiplied with time is equal to the change in kinetic energy.

When a spring is fixed at one end and a force is applied at the other end and as the applied force increases, deformation in the spring is

An object moves along a straight line path from P to Q under the action of a force $\left( {4\hat i - 3\hat j + 3\hat k} \right)$ N. If the coordinates of P and Q, in metres, are (3,3,-1) and (2,-1,4) respectively, then the work done by the force is

Three identical balls A,B and C are lying on a horizontal frictionless table as shown in figure. If ball A is imparted a velocity v towards B and C and the collisions are perfectly elastic, then finally

Given below are two statements: one is labelled as Assertion A and the other is labeled as Reason R.
Assertion A: Body $P$ having mass $M$ moving with speed $u\,$has head-on collision elastically with another body $Q$ having mass $m$ initially at rest. If $m < < M$, body $Q$ will have a maximum speed equal to $2u\,$ after collision.
Reason R: During elastic collision, the momentum and kinetic energy are both conserved.
In the Light of the above statements, choose the most appropriate answer from the options given below.

A mass of 50 kg is raised through a certain height by a machine whose efficiency is $90\%$, the energy is 5000 J. If the mass is now released, its KE on hitting the ground shall be

Assertion: The work done by the spring force in a cyclic process is zero.
Reason: Spring force is a conservative force.

A bob of mass $m$, suspended by a string of length $l_1$, is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass $m$ suspended by a string of length $\mathrm{l}_2$, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in the vertical plane, the ratio $\frac{\ell_1}{\ell_2}$ is

A motor can pump the water up to maximum height of 10m at the rate of $10\,kg\,{s^{ - 1}}$ . If efficiency of the motor is 0.8 then power of motor is

A rubber ball is dropped from a height of 5 m on a planet, where the acceleration due to gravity is not known. On bouncing it rises to 1.8 m. The ball loses its velocity on bouncing by a factor of

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

Choose the incorrect statement

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

A weightless thread can bear tension upto 37 N. A stone of mass 500 g is tied to it and revolved in a circular path of radius 4 m in a vertical plane. $\mathrm{If\;g} = 10\mathrm{\;m}{\mathrm{s}^{ - 2}},$ then the maximum angular velocity of the stone will be

A man is standing on a stationary car of mass $m$ placed on a smooth rail. The man starts walking with velocity $v$ relative to car. Find the mass of the man if work done by him when he moves along the rails is same when he walks normal to the rails

Velocity vector and acceleration vector in a uniform circular motion are related as

When two bodies collide elastically, the force of interaction between them is

A body is tied to one end of the string and whirled in a vertical circle, the physical quantity which remains constant is

A body of mass 50 kg is projected vertically upwards with velocity of 100 m/sec. 5 seconds after this body breaks into 20 kg and 30 kg. If 20 kg piece travels upwards with 150 m/sec, then the velocity of the block will be

A force of 5N, making an angle $\theta$ with the horizontal, acting on an object displaces it by 0.4m along the horizontal direction. If the object gains kinetic energy of 1J, the horizontal component of the force is

Statement-I: If collision occurs between two elastic bodies their kinetic energy decreases during the time of collision.
Statement-II: During collision intermolecular space decreases and hence elastic potential energy increases.

In uniform circular motion, the velocity vector and acceleration vector are

A body of mass m kg is lifted by a man to a height of one metre in 30 sec. Another man lifts the same mass to the same height in 60 sec. The work done by them are in the ratio

From a building two balls A to B are thrown such that A is thrown upwards and B downwards (both vertically). If ${v_A}$ and ${v_B}$ are their respective velocities on reaching the ground, then