Work Done on & by the Object

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

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

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

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. $v-t$ graph of a particle moving along x axis is shown in figure. Mass of the particle = 4 kg. Work done by all the forces acting on particle between $t=3$ to $t=6$ is

1. 12 J
2. 24 J
3. 8 J
4. 32 J

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

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

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 the figure. Work done by the normal reaction on the block in time $t$ is:

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

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

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. $5\text{J}$
4. Zero

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. $4\text{J}$
3. $-4\text{J}$
4. $-4.5\text{J}$

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

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. 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 $60\text{kg}$ 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 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. $110\text{J}$
2. $\frac{80}{3}\text{J}$
3. $\frac{95}{2}\text{J}$
4. Zero

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 the figure. Work done by the normal reaction on the block in time $t$ is:

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