Work Done on & by the Object

Q.

An elevator of total mass (elevator + passenger) $1800kg$ is moving up with a constant speed of $2m{s}^{-1}$ . A frictional force of $2000N$ is opposing its motion. The minimum power delivered by the motor to the elevator is [Take $g=10m{s}^{-2}$]

1. 36 kW

2. 4 kW

3. 40 kW

4. -40 kW

Q. A block of mass $m$ is kept on a platform which starts from rest with constant acceleration $\frac{g}{2}$ upwards as shown in figure. Work done by normal reaction on block in time $t$ is

1. $\frac{m{g}^2{t}^2}{8}$
2. $\frac{3m{g}^2{t}^2}{8}$
3. 0
4. $-\frac{m{g}^2{t}^2}{8}$

Q. $300\text{J}$ of work done in sliding a $2\text{kg}$ block up the inclined plane of height $10\text{m}$ with constant velocity. The work done against friction is (Take $g=10{\text{m/s}}^2$)

1. Zero $\text{J}$
2. $200\text{J}$
3. $500\text{J}$
4. $100\text{J}$

Q.

The descending pulley shown in figure (10-E7) has a radius 20 cm and moment of inertia 0.20 kg-m${}^2$. The fixed pulley is light and the horizontal plane frictionless. Find the acceleration of the block if its mass is 1.0 kg.

Q. A string is used to pull a block of mass $m$ vertically up by a distance $h$ at a constant acceleration $\frac{g}{4}$. The work done by the tension in the string is

1. $+\frac{3}{4}mgh$
2. $-\frac{1}{4}mgh$
3. $+\frac{5}{4}mgh$
4. $+mgh$

Q. In the shown pulley-block system, strings are light. Pulleys are massless and smooth and system is released from rest. In $0.6$ second, what is the work done by gravity on $20\text{kg}$ and $10\text{kg}$ block respectively ?
Take $[g=10{\text{m/s}}^2]$

1. $30\text{J};120\text{J}$
2. $-240\text{J};60\text{J}$
3. $120\text{J};30\text{J}$
4. $240\text{J};-60\text{J}$

Q. Figure gives the acceleration of a $2.0\text{kg}$ body as it moves from rest along $x-$ axis, while a variable force acts on it from $x=0\text{m}$ to $x=9\text{m}$.
The work done by the force on the body when it reaches $x=4\text{m}$ and $x=7\text{m}$ is

1. $21\text{J}$ and $33\text{J}$ respectively
2. $21\text{J}$ and $15\text{J}$ respectively
3. $42\text{J}$ and $60\text{J}$ respectively
4. $42\text{J}$ and $30\text{J}$ respectively

Q. A $60\text{kg}$ weight is dragged on a horizontal surface by a rope upto $2\text{m}$ with constant speed. If the coefficient of friction is $\mu =0.5$, the angle of rope with the surface is ${60}^{\circ }$ and $g=9.8{\text{m/sec}}^2$, then work done by rope on the block is

1. $294\text{J}$
2. $315\text{J}$
3. $588\text{J}$
4. $197\text{J}$

Q.

A string of length L and mass M is lying on a horizontal table. A force F is applied at one of its ends. Tension in the string at a distance y from the end at which the force applied is:

1. $F$

2. $\frac{F(L-Y)}{M}$

3. $Zero$

4. $\frac{F(L-Y)}{L}$

Q. One end of a light rope is tied directly to the ceiling. A man of mass $M$ initially at rest on the ground starts climbing the rope upto a height $l$. From the time he starts at rest on the ground to the time he is hanging at rest at a height $l$, how much work was done on the man by the rope?

1. $0$
2. $Mgl$
3. $-Mgl$
4. It depends on how fast the man goes up.

Q. A particle of mass $20\text{g}$ is thrown vertically upwards with a speed of $10\text{m/s}$. Find the work done by the gravity during the time of ascent of the particle.

1. $1\text{J}$
2. $-1\text{J}$
3. $2\text{J}$
4. $-2\text{J}$

Q. An object of mass $m=5\text{kg}$ is being pulled up a rough inclined plane which is at ${45}^{\circ }$ to the horizontal. The object is pulled at a constant speed of $0.8\text{m/s}$ by a force which acts parallel to the inclined plane. The coefficient of kinetic friction between the object and the plane is $0.2$. Calculate the work done by the force in pulling the block by $0.5\text{m}$. ($g=10{\text{m/s}}^2$)

1. $21.2\text{J}$
2. $23.2\text{J}$
3. Zero
4. $17.68\text{J}$

Q. A particle of mass 100g is thrown vertically upwards with a speed of 5 m/s. The work done by the force of gravity during the time, the particle goes up is,

1. -0.5 J
2. -1.25J
3. 1.25J
4. 0.5J

Q. A block of mass $2\text{kg}$ is being brought down by a string. If the block acquires a speed of $1\text{m/s}$ in dropping down $25\text{cm}$, find the work done by the tension in the process.

1. $-\text{16 J}$
2. $-4.5\text{J}$
3. $4\text{J}$
4. $-4\text{J}$

Q. A situation may be described by using different sets of coordinate axes having different orientations. Magnitude of which of the following do not depend on the orientation of the axis ?

1. Dot product
2. Cross product
3. Work done by force
4. Torque by a force

Q. Force - displacement curve for a body in one dimensional motion is as shown in the figure.

Work done by the force in displacing the body from displacment zero to $6\text{m}$ is given by

1. $10\text{J}$
2. zero
3. $60\text{J}$
4. $20\text{J}$

Q. A force $F=-\frac{k}{x^2}(x\ne 0)$ acts on a particle in $x-$direction. Find the work done by this force in displacing the particle from $x=+a$ to $x=+2a.$ Here $k$ is a positive constant.

1. $\frac{k}{a}$
2. $\frac{k}{a}$
3. $\frac{k}{a}$
4. $-\frac{k}{2a}$

Q. In the figure as shown two blocks are connected by a string over a pulley.

Calculate the total work done by tension force on the system for $1\text{m}$ distance covered.

1. $\frac{80}{3}\text{N}$
2. $-\frac{80}{3}\text{N}$
3. Zero
4. None

Q. A block of mass $3\text{kg}$ slides on a rough fixed inclined plane of ${37}^{\circ }$angle , having coeffecient of friction $0.5$. The resultant force exerted by plane on the block is -

1. $6\sqrt{5}\text{N}$
2. $8\sqrt{5}\text{N}$
3. $10\sqrt{5}\text{N}$
4. $12\sqrt{5}\text{N}$

Q. A body constrained to move along the $z$-axis of a co-ordinate system is subjected to a constant force $\overrightarrow{F}=(-\hat{i}+2\hat{j}+3\hat{k})\text{N}$. What is the work done by the force in moving the body over a distance of $4\text{m}$ along the $z$-axis?

1. $12\text{J}$
2. $8\text{J}$
3. $16\text{J}$
4. $6\text{J}$

Q. Two opposite charge particles under mutual force of attraction are given uniform initial velocity of same magnitude in opposite direction. They lose $220\text{J}$ of their $K.E$ after travelling $2\text{m}$ distance. Calculate the work done by internal force

1. Zero
2. $-220\text{J}$
3. $+220\text{J}$
4. $110\text{J}$

Q. A position dependent force $F=(x^2-3)\text{N}$ acts on a small body of mass $2\text{kg}$ and displaces it from $x=0$ to $x=5\text{m}$. The work done is

1. $\frac{95}{2}\text{J}$
2. Zero
3. $\frac{80}{3}\text{J}$
4. $110\text{J}$

Q. An object of mass $m=5\text{kg}$ is being pulled up a rough inclined plane which is at ${45}^{\circ }$ to the horizontal. The object is moving at an acceleration of $2{\text{m/s}}^2$ along the inclined plane. The coefficient of kinetic friction between the object and the plane is $0.2$. Calculate the total work done in pulling the block by $0.5\text{m}$. ($g=10{\text{m/s}}^2$)

1. $7\text{J}$
2. $10\text{J}$
3. Zero
4. $5\text{J}$

Q.

A bead B of mass ‘m’ can travel without friction on a smooth horizontal wire xx’. The bead is connected to a block of identical mass by an ideal string passing over an ideal pulley. The system, as shown, is in vertical plane.

System is initially released from rest in the position shown. Initial acceleration of block A is:

1. zero

2. 
   $\frac{g}{2}$

3. $\frac{3g}{7}$

4. $\frac{4g}{7}$

Q. Two change particles having $+ve$ charge are held together at a certain distance. When they are released they start moving away from each other and gain $150\text{J}$ of their $KE$. Determine the total work done by internal forces.

1. $+150\text{J}$
2. Zero
3. None
4. $-150\text{J}$

Q. On a certain planet, a stone weighing $2\text{kg}$ is thrown vertically downwards with a velocity of $5\text{m/s}$ from a height of $30\text{m}$. It took $4\text{s}$ to reach the ground. Calculate the work done by gravity.

1. $-75\text{J}$
2. $60\text{J}$
3. $-60\text{J}$
4. $75\text{J}$

Q. A force of $5\text{N}$, making an angle $\theta$ with the horizontal, acting on an object and displaces it by $0.4\text{m}$ along the horizontal direction. If the work done by the force is $1\text{J}$, then the horizontal component of the force is

1. $1.5\text{N}$
2. $2.5\text{N}$
3. $3.5\text{N}$
4. $4.5\text{N}$

Q. In the figure, force $F=\alpha t$. Which of the following represents the acceleration-time graph of both the blocks? ($a_1$ and $a_2$ are the accelerations of blocks $m_1$ and $m_2$ respectively)

1. 
2. 
3. 
4. 

Q. A person holds a bucket of weight $60N$. He walks $7m$ along the horizontal path and then climbs up a vertical distance of $5m$. The work done by the man is:

1. $300J$
2. $420J$
3. $720J$
4. $noneofthese$

Q. A rigid body of mass m is moving on circular path of radius r & with a constant speed v, net force on body is F, then during half rotation work done by F is,

1. F$\left(\pi r\right)$
2. zero
3. F(r$\sqrt{2}$)
4. F(2r)