Work-energy-power practice · Mixed difficulty

A gun fires bullet each of mass 1 g with velocity of $10\;\mathrm{m}{\mathrm{s}^{ - 1}}$ by exerting a constant force of 5 g weight. Then the number of bullets fired per second is (Take $g = 10\;\mathrm{m}{\mathrm{s}^{ - 2}})$

A force of $\left( {7\hat i + 6\hat k} \right)$ N makes a body move on a rough plane with a velocity of $\left( {3\hat j + 4\hat k} \right)m{s^{ - 1}}$. Calculate the power in watt

Assertion: Potential energy is possible only in conservative force field.
Reason: Potential energy is a relative quantity but K.E. is an absolute quantity.

Work done when a force, $\mathrm{\vec F} = \left( {\hat i + 2\hat j + 3\hat k} \right)$ N acting on a particle takes it from the point ${\mathrm{\vec r}_1} = \left( {\hat i + \hat j + \hat k} \right)$ m to the point ${\mathrm{\vec r}_2} = \left( {\hat i + \hat j + 2\hat k} \right)$

When a force is applied on a moving body, its motion is retarded. Then the work done is

When a spring is extended by 2 cm energy stored is 100 J. When extended by further 2 cm, the energy increases by

Maximum work will be done if the angle between force applied and displacement produced is

A particle free to move along the x-axis has potential energy given by $U\left( x \right) = k\left[ {1 - \exp \left( { - {x^2}} \right)} \right]$ for $- \infty \le x \le + \infty$ where k is a positive constant of appropriate dimensions. Then

A body moves a distance of 20 m along a straight line under the action of a 5 N force. If the work done is 25 J then the angle between the force and direction of motion of the body is

During a heavy rain, hailstones of average size $1.0 \mathrm{~cm}$ in diameter fall with an average speed of $20 \mathrm{~m} / \mathrm{s}$. Suppose 2000 hailstones strike every square meter of a $10 \mathrm{~m} \times 10 \mathrm{~m}$ roof perpendicularly in one second and assume that the hailstones do not rebound. Calculate the average force exerted by the falling hailstones on the roof. Density of a hailstone is $900 \mathrm{~kg} / \mathrm{m}^3$.

The potential energy of a 1 kg particle free to move along the x-axis is given by $V\left( x \right) = \left( {\frac{{{x^4}}}{4} - \frac{{{x^2}}}{2}} \right)\mathrm{J}$.The total mechanical energy of particle is 2 J. Then, the maximum speed $\left( {\mathrm{in\;m}{\mathrm{s}^{ - 1}}} \right)$ is

A particle is taken from point A to point B under the influence of a force field. Now it is taken back from B to A and it is observed that the work done in taking the particle from A to B is not equal to the work done in taking it from B to A. If $W_{n c}$ and $W_c$ is the work done by non - conservative forces and conservative forces present in the system respectively, $\Delta U$ is the change in potential energy, $\Delta k$ is the change in kinetic energy, then choose the correct option

If the heart pushes 1 cc of blood in 1 s under pressure 20000$N{m^{ - 2}}$ ,the power of heart is

Two identical balls $A$ and $B$ having velocities of $0.5\,m/s$ and $- 0.3\,m/s$ respectively collide elastically in one dimension. The velocities of $B$ and $A$ after the collision respectively will be

Statement-I: The workdone in pushing a block is more than the work done in pulling the block on a rough surface.
Statement-II: In the pushing condition normal reaction in more.

Two bodies of masses m and 2m have same momentum. Their respective kinetic energies ${E_1}\,and\,{E_2}$ are in the ratio

A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kg of energy. The initial velocity of the shell is

A mass of $2 \mathrm{~kg}$ is whirled in a horizontal circle by means of a string at an initial speed of $5 \mathrm{~rev}\mathrm{~min}^{-1}$. Keeping the radius constant the tension in the string is doubled. The new speed is nearly

10 L of water per second is lifted from well through 20 m and delivered with a velocity of $10m{s^{ - 1}},$ then the power of the motor is

Statement I: For the stable equilibrium force has to be zero and potential energy should be minimum.

Statement II: For the equilibrium it is not necessary that the force is not zero.

A small sphere of mass m, moving with a constant velocity v, hits another stationary sphere of same mass. If e be the coefficient of restitution, then ratio of velocities ${v_1}\,and\,{v_2}$ of two spheres after collision will be

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

Internal forces acting in a system of particle can
change

A water pump lifts water from a level $10 \mathrm{~m}$ below the ground. Water is pumped at a rate of 30 kg/minute with negligible velocity. Calculate the minimum horsepower the engine should have to do this.

A spring of constant $100 \mathrm{~N} / \mathrm{m}$ is stretched by applying equal forces each of magnitude $F$ at the two ends. The energy stored in the spring is $200 \mathrm{~J}$. Now, spring is cut into two equal parts and one of the part is stretched by applying equal forces each of magnitude $F$ at the two ends. The energy stored is

A particle acted upon by constant forces $4\hat i + \hat j - 3\hat j\,and\,3\hat i + \hat j - \hat k$ is displaced from the point $\hat i + 2\hat j + 3\hat k$ to the point $5\hat i + 4\hat j + \hat k$.The total work done by the forces in SI unit is

A body of mass 5 kg strikes another body of mass 2.5 kg initially at rest. The bodies after collision coalesce and begin to move as a whole with a kinetic energy of 5 J. The kinetic energy of the first body before collision is

A bus can be stopped by applying a retarding force $F$ when it is moving with speed $v$ on a level road. The distance covered by it before coming to rest is $s$. If the load of the bus increases by $50 \%$ because of passengers, for the same speed and same retarding force. the distance covered by the bus to come to rest shall be

A body is moving with a constant speed $v$ in a circle of radius $r$. Its angular acceleration is

Statement I: On banked curved road, vertical component of normal reaction provides the necessary centripetal force.

Statement II: Centripetal force is always required for turning.