If a force $(\beta \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}) \mathrm{N}$ acting on a body displaces it through $(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+1 \hat{\mathbf{k}}) \mathrm{m}$, then the work done by the force on the body is

A body is projected vertically upwards with a velocity of $20 \mathrm{~ms}^{-1}$. If the potential energy of the body at a height of 5 m from the ground is 100 J , then the kinetic energy of the body at a height of 10 m from the ground is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

If a constant force of $(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}) \mathrm{N}$ acting on a body of mass 5 kg displaces it from $(3 \hat{\mathbf{i}}-4 \hat{\mathbf{k}}) \mathrm{m}$ to $(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})$ m , then the work done by the force on the body is

A motor can pump 7560 kg of water per hour from a well of depth 100 m . If the efficiency of the pump is $70 \%$, then power of the pump is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

If the potential energy of a particle of mass 0.1 kg moving along $X$-axis is $5 x(x-4) \mathrm{J}$, then the speed of the particle is maximum at a position of

If a force $\mathbf{F}=(3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}) \mathrm{N}$ acting on a body displaces it from point $(1 \mathrm{~m}, 2 \mathrm{~m})$ to point $(2 \mathrm{~m}, 0 \mathrm{~m})$, then work done by the force is

If a force of $\left(6 x^2-4 x\right) \mathrm{N}$ acts on a body of mass 10 kg , then work to be done by the force in displacing the body from $x=2 \mathrm{~m}$ to $x=4 \mathrm{~m}$ is

A circular well of diameter 2 m has water upto the ground level. If the bottom of the well is at a depth of 14 m , the time taken in seconds to empty the well using a 1.4 kW motor is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A car of mass 2000 kg is accelerating from rest. If its engine is supplying constant power of 10 kW , then the velocity of the car at a time of 10 s is

A body of mass ' $M$ ' is moving with a uniform speed of ' $V^{\prime}$ on a frictionless horizontal surface under the influence of two forces $F_1$ and $F_2$ as shown in the figure. The net power of the system is

Two bodies $A$ and $B$ of masses 20 kg and 5 kg respectively are at rest. Due to the action of a force of 40 N separately, if the two bodies acquire equal kinetic energies in times $t_A$ and $t_B$ respectively, then $t_A: t_B=$

A crane of efficiency $80 \%$ is used to lift 8000 kg of coal from a mine of depth 108 m . If the time taken by the crane to lift the coal is one hour, then the power of the crane (in kW ) is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A train of mass $10^6 \mathrm{~kg}$ is moving at a constant speed of $108 \mathrm{~km} / \mathrm{h}$. If the frictional force acting on it is 0.5 N per 100 kg , then the power of the train is

A body is moving along a straight line under the influence of a constant power source. If the relation between the displacement $(s)$ of the body and time $(t)$ is $s \propto t^x$, then $x=$

A body is projected at an angle of $60^{\circ}$ with the horizontal. If the initial kinetic energy of the body is $X$, then its kinetic energy at the highest point is

The bob of a simple pendulum of length 200 cm is released from horizontal position. If $10 \%$ of its initial energy is lost due to air resistance, then the speed of bob at the mean position is

(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

The power required for an engine to maintain a constant speed of $50 \mathrm{~ms}^{-1}$ for a train of mass $3 \times 10^6 \mathrm{~kg}$ on rough rails is

(The coefficient of kinetic friction between the rails and wheels of the train is 0.05 and acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

The linear momentum of a body of mass 8 kg is $24 \mathrm{~kg} \mathrm{~ms}^{-1}$. If a constant force of 24 N acts on the body in the direction of motion of the body for a time of 3 s , then the increase in the kinetic energy of the body is

A person holds a ball of mass 0.25 kg in his hand and throws it, so that it leaves his hand with a speed of $12 \mathrm{~ms}^{-1}$. In this process, if his hand moved through a distance of 0.9 m , then the net force acted on the ball is

A particle of mass $m$ at rest on a rough horizontal surface with a coefficient of friction $\mu$ is given a

velocity $u$. The average power imparted by friction before it stops

A body thrown vertically upwards from the ground reaches a maximum height $H$. The ratio of the velocities of the body at heights $\frac{3 H}{4}$ and $\frac{8 H}{9}$ from the ground is

A $4 \mathrm{~kg}$ mass is suspended as shown in figure. All pulleys are frictionless and spring constant $k$ is $8 \times 10^3 \mathrm{Nm}^{-1}$. The extension in spring is $\left(g=10 \mathrm{~ms}^{-2}\right)$

A small disc of mass $m$ slides down with initial velocity zero from the top $(A)$ of a smooth hill of height $H$ having a horizontal portion $(BC)$ as shown in the figure. If the height of the horizontal portion of the hill is $h$, then the maximum horizontal distance covered by the disc from the point $D$ is

A block of mass 50 kg is pulled with a constant speed of $4 \mathrm{~ms}^{-1}$ across a horizontal floor by an applied force of 500 N directed $30^{\circ}$ above the horizontal. The rate at which the force does work on the block in watt is

A ball of mass 300 g is dropped from a height 10 m above a sandy ground. On reaching the ground, it penetrates through a distance 1.5 m in sand and finally stops. The average resistance offered by the sand to oppose the motion is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$)

A mass of 1 kg falls from a height of 1 m and lands on a massless platform supported by a spring having spring constant $15 \mathrm{~Nm}^{-1}$ as shown in the figure. The maximum compression of the spring is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$)

A bead of mass 400 g is moving along a straight line under a force that delivers a constant power 1.2 W to the bead. If the bead is initially at rest, the speed it attains after 6 s in $\mathrm{ms}^{-1}$

An engine develops 20 kW of power. How much time will it take to lift a mass of 200 kg to a height of 40 m? (g = 10 ms$^{-2}$ )

Two bodies having kinetic energy in the ratio 4 : 1, are moving with same linear velocity. The ratio of their masses is

Water is falling on the blades of a turbine from a height of $25 \mathrm{~m}$ and $3 \times 10^3 \mathrm{~kg}$ of water pours on the blade per minute. If the whole of energy is transferred to the turbine, then power delivered is

The range of a projectile is 100 m. Its kinetic energy will be maximum after covering a distance of

When a force F = 17 $-$ 2x + 6x$^2$N acts on a body of mass 2 kg and displaces it from x = 0 m to x = 8 m, the work done is

A rifle bullet loses $\left(\frac{1}{25}\right)$th of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is

A uniform chain has a mass m and length $l$. It is held on a frictionless table with one-sixth of its length hanging over the edge. The work done in just pulling the hanging part back on the table is

What is the shape of the graph between speed and kinetic energy of a body?

A quarter horse power motor runs at a speed of 600 rpm. Assuming 60% efficiency, the work done by the motor in one rotation is

A body of mass 8 kg, under the action of a force, is displaced according to the equation, $s=\frac{t^2}{4}$ m, where t is the time. Find the work done by the force in the first 4 s.