Work by Multiple Forces

Q. The length of an elastic string is ‘a’ metre when the tension is 4N and ‘b’ metre when the tension is 5N. The length, in metre, when the tension is 9 N, is

1. (5b-4a)
2. (9b-9a)
3. (a+b)
4. (4b-5a)

Q. A body of mass m kg is lifted by a man to a height of one metre in 30 sec. Another man lifts the same mass to the same height in 60 sec. The work done by them(approximately) are in the ratio

1. 1 : 2
2. 2 : 1
3. 1 : 1
4. 4 : 1

Q. A spring is fixed at the bottom end of an incline of inclination ${37}^{\circ }$. A small block of mass $2\text{kg}$ starts slipping down the incline from a point $4.8\text{m}$ away (along the inclined plane) from the spring. The block compresses the spring by $20\text{cm}$, stops momentarily and then rebounds through a distance of $1\text{m}$ up the incline. Then:

1. Friction co-efficient between the plane and block is $0.7$
2. Friction co-efficient between the plane and block is $0.5$
3. Spring constant is $1000\text{N/m}$
4. Spring constant is $800\text{N/m}$

Q. A spring is compressed between two toy carts of masses $m_1$ and $m_2$. When the toy carts are released, the spring exerts on each toy cart equal and opposite forces for the same time $t$. If the coefficients of friction $\mu$ between the ground and the toy carts are equal, then the displacements of the toy carts are in the ratio

1. $\frac{s_1}{s_2}=\frac{m_2}{m_1}$
2. $\frac{s_1}{s_2}=\frac{m_1}{m_2}$
3. $\frac{s_1}{s_2}={\left(\frac{m_2}{m_1}\right)}^2$
4. $\frac{s_1}{s_2}={\left(\frac{m_1}{m_2}\right)}^2$

Q.

Name a physical quantity which has same unit as of work ?

Q. A particle is shifted from point $(0,0,1\text{m})$ to $(1\text{m},1\text{m},2\text{m})$, under the simultaneous action of several forces. Two of the forces are $\overrightarrow{F_1}=(2\hat{i}+3\hat{j}-\hat{k})\text{N}$ and $\overrightarrow{F_2}=(\hat{i}-2\hat{j}+2\hat{k})\text{N}$. Find the work done by these two forces

1. $5\text{J}$
2. $10\text{J}$
3. $12\text{J}$
4. $7\text{J}$

Q. A constant force $10\text{N}$ acts on a ball of mass $2\text{kg}$ for $2\text{s}$ . Then another force $18\text{N}$ acts on the same ball for $\frac{10}{9}\text{second}$. If ball is initially at rest, then find the total work done.

1. $400\text{J}$
2. $300\text{J}$
3. $200\text{J}$
4. $100\text{J}$

Q. Three forces are acting on the block as shown in figure.


Find work done by net force if block moves $10\text{m}$ in horizontal direction. Given that $[F_1=20\text{N},F_2=5\sqrt{2}\text{N},F_3=10\text{N}]$

1. $50\text{J}$
2. $100\text{J}$
3. $75\text{J}$
4. $\text{No work done as friction is absent}$

Q. Three forces act on block as shown in figure.

Find work done by net force, if the block moves $10\text{m}$ in horizontal direction
Given magnitudes of forces are
[$F_1=20\text{N},F_2=5\sqrt{2}\text{N},F_3=10\text{N}$]

1. $50\text{J}$
2. $100\text{J}$
3. $75\text{J}$
4. Work done is equal to zero as there is no friction.

Q.

A block of mass 2 kg is moving with a speed of $10m{s}^{-1}$ on a rough horizontal floor till it stops. Determine the work done against the friction.

Q. A constant force $\overrightarrow{F_1}=(2\hat{i}-4\hat{j})\text{N}$ displaces a particle from $(1,-1,2)$ to $(-1,-1,3)$ and then another force $\overrightarrow{F_2}=(3\hat{i}+4\hat{j})\text{N}$ displaces it from $(-1,-1,3)$ to $(5,5,5)$ (displacement being measured in metres). Find the total work done.

1. $38\text{J}$
2. $46\text{J}$
3. $40\text{J}$
4. $30\text{J}$

Q. The resultant of two forces has magnitude of $20N$ . if one of the forces is of magnitude $20\sqrt{3}N$ and makes an angle of ${30}^{\circ }$ with the resultant then, the other forces must be of magnitude

1. $10\sqrt{3}N$
2. $20N$
3. $20\sqrt{3}N$
4. $10N$

Q. A spring is fixed at the bottom end of an incline of inclination ${37}^{\circ }$. A small block of mass $2\text{kg}$ starts slipping down the incline from a point $4.8\text{m}$ away (along the inclined plane) from the spring. The block compresses the spring by $20\text{cm}$, stops momentarily and then rebounds through a distance of $1\text{m}$ up the incline. Then:

1. Friction co-efficient between the plane and block is $0.7$
2. Friction co-efficient between the plane and block is $0.5$
3. Spring constant is $1000\text{N/m}$
4. Spring constant is $800\text{N/m}$

Q. Figure shows three forces applied to a block that moves leftward by $3\text{m}$ over a smooth floor. The magnitudes of force are $F_1=5\text{N},F_2=9\text{N}$ and $F_3=3\text{N}$. The net work done on the block by the three forces will be

1. $1.5\text{J}$
2. $4.5\text{J}$
3. $3\text{J}$
4. $3.6\text{J}$

Q. Three constant forces are applied on a body are given as $\overrightarrow{F_1}=3\hat{i}\text{N},\overrightarrow{F_2}=4\hat{j}\text{N},\overrightarrow{F_3}=6\hat{k}\text{N}$.
If these forces displace the body by $5\text{m}$ in negative $y$-axis direction from origin. Then total work done by the forces is

1. $20\text{N}$
2. $65\text{N}$
3. $-5\text{N}$
4. $-20\text{N}$

Q. Three forces are acting on the block as shown in figure.


Find work done by net force if block moves $10\text{m}$ in horizontal direction. Given that $[F_1=20\text{N},F_2=5\sqrt{2}\text{N},F_3=10\text{N}]$

1. $50\text{J}$
2. $100\text{J}$
3. $75\text{J}$
4. $\text{No work done as friction is absent}$

Q. The total work done by three forces on a block is $60\text{J}$. If block is displaced by a force from position $A(1,2,3)$ to $B(7,6,5)$. Find out the third force if the other two forces are $\overrightarrow{F_1}=(7\hat{i}+3\hat{j}+2\hat{k})\text{N}$, and $\overrightarrow{F_2}=(-2\hat{i}+2\hat{j}+\hat{k})\text{N}$.
Assume that $\overrightarrow{F_3}$ is perpendicular to $XY$ plane.

1. $\overrightarrow{F_3}=\hat{k}$
2. $\overrightarrow{F_3}=2\hat{k}$
3. $\overrightarrow{F_3}=3\hat{k}$
4. $\overrightarrow{F_3}=4\hat{k}$

Q. In the arrangement shown, the block is released from rest from $x=0$ (when the spring was in its natural length), on a rough incline surface having $\mu =0.5x.$ The maximum elongation in the spring will be,

1. $1\text{m}$
2. $1.5\text{m}$
3. $2\text{m}$
4. $2.5\text{m}$

Q. Two long, thin, parallel conductors, separated by a distance d carry currents $i_1$ and $i_2$. The force acting on unit length of any one conductor is F :

1. F is the same for both conductors
2. F is attractive, if $i_1$ and $i_2$ flow in the opposite directions
3. F is attractive, if $i_1$ and $i_2$ flow in the same directions
4. F is the different for the two conductors

Q. A constant force $10\text{N}$ acts on a ball of mass $2\text{kg}$ for $2\text{s}$ . Then another force $18\text{N}$ acts on the same ball for $\frac{10}{9}\text{second}$. If ball is initially at rest, then find the total work done.

1. $400\text{J}$
2. $300\text{J}$
3. $200\text{J}$
4. $100\text{J}$

Q.

Match the column A with column B

Column 1	Column 2
Work done by a weight lifter in bringing down a weight from a height	Work done is negative
Work done by the gravitational force on a freely falling body.	Work done is positive
A body moving on a rough surface	Mechanical energy is conserved
A ball moving on a smooth surface.	Mechanical energy is not conserved

Q.

Multiple constant forces $F_1,......F_i$ are acting on an object of mass 'm' and produce a displacement S, with an acceleration a. Which of the following statements is true.

1. Work done on the object is ${\sum }_{i=1}^n\overrightarrow{F_i}.\overrightarrow{S}$

2. Work done on the object is $\left({\sum }_{i=1}^n\overrightarrow{F_i}\right).\overrightarrow{S}$

3. Work done on the object is $m\overrightarrow{a}.\overrightarrow{S}$

4. If all the forces are acting in the same direction, then work done will be maximum

Q. A particle is shifted from point $(0,0,1\text{m})$ to $(1\text{m},1\text{m},2\text{m})$, under the simultaneous action of several forces. Two of the forces are $\overrightarrow{F_1}=(2\hat{i}+3\hat{j}-\hat{k})\text{N}$ and $\overrightarrow{F_2}=(\hat{i}-2\hat{j}+2\hat{k})\text{N}$. Find the work done by these two forces

1. $7\text{J}$
2. $5\text{J}$
3. $10\text{J}$
4. $12\text{J}$

Q. A cord is used to lower vertically a block of mass $M$ through distance $d$ at a constant downward acceleration of $\frac{g}{4}$. Then, the work done by the cord on the block is -

1. $\frac{Mgd}{4}$
2. $-\frac{Mgd}{4}$
3. $\frac{3Mgd}{4}$
4. $-\frac{3Mgd}{4}$

Q. A constant force $\overrightarrow{F_1}=(2\hat{i}-4\hat{j})\text{N}$ displaces a particle from $(1,-1,2)$ to $(-1,-1,3)$ and then another force of $\overrightarrow{F_2}=(3\hat{i}+4\hat{j})\text{N}$, displaces it from $(-1,-1,3)$ to $(5,5,5)$ (displacements being measure in metre). Find the total work done.

1. $46\text{J}$
2. $38\text{J}$
3. $40\text{J}$
4. $36\text{J}$

Q. The figure shows a spring fixed at the bottom end of an incline of inclination ${37}^{\circ }$. A small block of mass $2\text{kg}$ starts slipping down the incline from a point $4.8\text{m}$ away from the spring. The block compresses the spring by $20\text{cm}$, stops momentarily and then rebounds through a distance of $1\text{m}$ up the incline. Find the friction coefficient between the plane and the block and the spring constant of the spring.
Take $g=10{\text{m/s}}^2$.

1. $0.25,100\text{N/m}$
2. $0.25,1000\text{N/m}$
3. $0.5,100\text{N/m}$
4. $0.5,1000\text{N/m}$

Q. In the following arrangement, an object of mass 1.2 kg is at rest at point p. If N and the F are the reaction and the force of friction, then $(g=10m{s}^{-1})$.

1. $N=6\sqrt{3}N,F=6N$
2. $N=6N,F=6\sqrt{3}N$
3. $N=3N,F=3\sqrt{3}N$
4. $N=6N,F=3N$
   

Q.

Multiple constant forces $F_1,......F_i$ are acting on an object of mass 'm' and produce a displacement S, with an acceleration a. Which of the following statements is true.

1. Work done on the object is ${\sum }_{i=1}^n\overrightarrow{F_i}.\overrightarrow{S}$

2. Work done on the object is $\left({\sum }_{i=1}^n\overrightarrow{F_i}\right).\overrightarrow{S}$

3. Work done on the object is $m\overrightarrow{a}.\overrightarrow{S}$

4. If all the forces are acting in the same direction, then work done will be maximum

Q. In a simple pendulum, work done by tension is non zero.

1. False
2. True

Q. In the arrangement shown, the block is released from rest from $x=0$ (when the spring was in its natural length), on a rough incline surface having $\mu =0.5x.$ The maximum elongation in the spring will be,

1. $1\text{m}$
2. $2.5\text{m}$
3. $2\text{m}$
4. $1.5\text{m}$