Work, Energy and Power

A body of mass 0.5 kg is supplied with a power ' $P$ ' (in watt) which varies with time ' $f$ ' (in second) as $P=3 t^2+3$. If the velocity of the body at time $t=0$ is zero, then the velocity of the body at time $t=3 \mathrm{~s}$ is

If the kinetic energy of a body moving with a velocity of $(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-4 \hat{\mathrm{k}}) \mathrm{ms}^{-1}$ is 87 J , then the mass of the body is

A body of mass 500 g is falling from rest from a height of 3.2 m from the ground. If the body reaches the ground with a velocity of $6 \mathrm{~ms}^{-1}$, then the energy lost by the body due to air resistance is (Acceleration due to gravit...

The work done in displacing a particle from $y=a$ to $y=2 a$ by a force $-\frac{K}{y^2}$ acting along $Y$-axis is

A block of mass 0.5 kg is at rest on a horizontal table. The coefficient of kinetic friction between the table and the block is 0.2 . If a horizontal force of 5 N is applied on the block, the kinetic energy of the block in a time of 4 s is ...

The work done in increasing the diameter of a soap bubble from 2 cm to 4 cm is (Surface tension of soap solution $=3.5 \times 10^{-2} \mathrm{Nm}^{-1}$ )

A block of mass $m$ with an initial kinetic energy $E$ moves up an inclined plane of inclination $\theta$. If $\mu$ is the coefficient of friction between the plane and the body, the work done against friction before coming to rest is

A man of mass 80 kg goes to the market on a scooter of mass 100 kg with certain speed. On application of brakes, the stopping distance is $s_1$. The man returns home on the same scooter, with the same speed with a 60 kg bag of rice. If $s_2...

A constant force of $(8 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}) \mathrm{N}$ acting on a body of mass 2 kg displaces the body from $(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}) \mathrm{m}$ to $(4 \hat{\mathbf{i}...

A body thrown vertically upwards from the ground reaches a maximum height $h$. The ratio of the kinetic and potential energies of the body at a height $40 \%$ of $h$ from the ground is

A block kept on a frictionless horizontal surface is connected to one end of a horizontal spring of constant $100 \mathrm{Nm}^{-1}$ whose other end is fixed to a rigid vertical wall. Initially the block is at its equilibrium position. The b...

The work done in blowing a soap bubble of volume $V$ is $W$. The work done in blowing the bubble of volume 2 V from the same soap solution is

The kinetic energy of a body of mass 4 kg moving with a velocity of $(2 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-\hat{\mathbf{k}}) \mathrm{ms}^{-1}$ is

An engine is dragging a mass of 5000 kg with a velocity of $5 \mathrm{~ms}^{-1}$ along a smooth inclined plane of inclination 1 in 50 . Then the power of the engine is

A body of mass 3 kg is moving under the action of a force which causes a displacement of $\left(t^3 / 3\right) \mathrm{m}$, where $t$ is time in seconds. The work done by the force in first 2 sec is

A body is moved along a straight line by an engine which delivers a constant power. The distance moved by the body in time $t$ is proportional to

Two bodies of masses of 1 g and 4 g are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is

The displacement $s$ of a body of mass 3 kg under the action of a force is given by $s=\frac{t^3}{3}$, where $s$ is in metres and $t$ is in seconds. The work done by the force in the first two seconds is

While a person climbs stairs, the gravitational potential energy of the person increases. The source of this energy is

Statement I The slope of kinetic energy-displacement curve of a body in motion will be directly proportional to its acceleration.
Statement II From a height of 15 m , a ball is projected vertically upwards with a velocity of $30 \mathrm{~m}...

An object is moving in a straight line under the influence of a source of constant power. If $v$ and $t$ are velocity and time respectively, then

A pump on the ground floor of a building can pump up water to fill a tank of volume $36 \mathrm{~m}^3$ in 30 min . If the tank is 50 m above the ground, and the electric power consumed by the pump is 40 k W , the efficiency of the pump is
(...

A boat of mass 1000 kg goes from rest to speed 20.0 $\mathrm{m} / \mathrm{s}$ in 5.0 s . The water exerts a constant drag force and the acceleration of the boat is constant. If the average power required by the boat is 45000 W , then the ma...

A ball of mass 1 kg moves in a straight line with velocity $v=c x^\alpha$, where $c=1$ (SI unit) and $\alpha$ is a constant. If the work done by the net force during its displacement from $x=0$ to $x=4 \mathrm{~m}$ is 128 J , then the $\alp...

The potential energy of an object is $U(x)=\left(5 x^2-4 x^3\right) \mathrm{J}$, where $x$ is the position in metre. The position at which the force becomes zero is

The graph of potential energy $U(x)$ versus distance $x$ is shown in the following figure. The force $F$ versus distance $x$ graph will be represented by (assume, that the force is conservative)

A block of mass $m$ placed on a rough horizontal plane is pulled by a constant power $P$. The coefficient of friction between the block and the surface is $\mu$. The maximum velocity of the block will be

A force acts on a 30 g particle in such a way that the position of the particle as a function of time is given by $x=\alpha t^2$, where $x$ is in metre, $t$ is in seconds and $\alpha=1 \mathrm{m} / \mathrm{s}^2$. The work done during the fi...

Identify the incorrect statement.

An elevator of mass 500 kg is ascending upwards with a constant acceleration $a=2 \mathrm{~m} / \mathrm{s}^2$. What is the work done by the tension in the elevator cable during its climb by 12 m ? (Take, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A force of 4 N acts on a 10 kg body initially at rest. Let $W_1$ is work done by force during $0 \leq t \leq \mathrm{ls}$. Likewise $W_2$ is the work done by force during $\mathrm{l} \mathrm{s} \leq t \leq 2 \mathrm{~s}$, where $t$ is time ...

The block starts from rest as shown in the figure. Find the work done by force of 10 N and friction in the time 0 to 4 s . [Take, $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

Under action of force, a 2 kg body moves such that its position $x$ as function of time $t$ is given by $x=\alpha t^2 / 2$, where $x$ is in metre, $t$ is in seconds and $\alpha=1 \mathrm{~m} / \mathrm{s}^2$. The work done by the force in th...

A force acts on a body of mass 10 kg , resulting in its displacement given as $x=\left(\frac{t^3}{25}\right) \mathrm{m}$, where $t$ is the time in seconds. The work done by the force in 5 s is

When a body is acted upon by a resultant force, then the work done by the resultant force is equal to

A ball of mass $m=1 \mathrm{~kg}$ is thrown from the top of a building with initial velocity $\mathbf{v}=(20 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{i}}+(24 \mathrm{~m} / \mathrm{s}) \hat{\mathbf{j}}$ at time $t=0$. The change in the potenti...

A force $\mathbf{F}=(2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}) \mathrm{N}$ is applied on an object of mass $M$. What is the work done by this force in moving the object horizontally along the $X$-axis by 3 m ?