Net Force

Q. Five forces $\overrightarrow{F_1},\overrightarrow{F_2},\overrightarrow{F_3},\overrightarrow{F_4}$ and $\overrightarrow{F_5}$ are acting on a particle of mass $2.0\text{kg}$ so that it is moving with $4{\text{m/s}}^2$ in east direction. If $\overrightarrow{F_1}$ force is removed then the acceleration becomes $7{\text{m/s}}^2$ in north. Find the magnitude of acceleration of the block if only $\overrightarrow{F_1}$ is acting.

1. $16{\text{m/s}}^2$
2. $\sqrt{65}{\text{m/s}}^2$
3. $\sqrt{260}{\text{m/s}}^2$
4. $\sqrt{33}{\text{m/s}}^2$

Q. When forces $F_1,F_2,F_3$ are acting on a particle of mass $m$ such that $F_2$ and $F_3$ are mutually perpendicular, then the particle remains stationary. If the force $F_1$ is now removed then the magnitude of acceleration of the particle is

1. $\frac{F_1}{m}$
2. $\frac{F_2{F}_3}{m{F}_1}$
3. $\frac{(F_2-F_3)}{m}$
4. $\frac{F_2}{m}$

Q. A body of mass $5\text{kg}$ under the action of constant force $\overrightarrow{F}=F_x\hat{i}+F_y\hat{j}$ has velocity at $t=0\text{s}$ as $\overrightarrow{u}=(6\hat{i}-2\hat{j})\text{m/s}$ and at $t=10\text{s}$ as $\overrightarrow{v}=6\hat{j}\text{m/s}$. The force $F$ is

1. $(-3\hat{i}+4\hat{j})\text{N}$
2. $(-\frac{3}{5}\hat{i}+\frac{4}{5}\hat{j})\text{N}$
3. $(3\hat{i}-4\hat{j})\text{N}$
4. $(\frac{3}{5}\hat{i}-\frac{4}{5}\hat{j})\text{N}$

Q. Ten coins are placed on top of each other on a horizontal table. If the mass of each coin is $10\text{gm}$, what is the magnitude and direction of the force on the 7th coin (counted from the bottom) due to all the coins above it? Take $g=10m/s^2$

1. 0.3 N downwards
2. 0.3 N upwards
3. 0.7 N downwards
4. 0.7 N upwards

Q. An object of mass $M$ is kept on a rough table as seen from above. Forces are applied as shown. Find the direction (from the vertical) of static friction if the object does not move.

1. ${30}^{\circ }$
2. ${37}^{\circ }$
3. ${45}^{\circ }$
4. ${53}^{\circ }$

Q. Ten coins are placed on top of each other on a horizontal table. If the mass of each coin is $10\text{gm}$, what is the magnitude and direction of the force on the 7th coin (counted from the bottom) due to all the coins above it? Take $g=10m/s^2$

1. 0.3 N downwards
2. 0.3 N upwards
3. 0.7 N downwards
4. 0.7 N upwards

Q. A $2\text{kg}$ object is subjected to three forces that give it an acceleration $\overrightarrow{a}=-\left(8\hat{i}\right){\text{m/s}}^2$. If two of the three forces are ${\overrightarrow{F}}_1=(30\hat{i}+16\hat{j})\text{N}$ and ${\overrightarrow{F}}_2=(-12\hat{i}+8\hat{j})\text{N}$, find the third force ($\text{in N}$).

1. $34\hat{i}+24\hat{j}$
2. $-34\hat{i}-24\hat{j}$
3. $18\hat{i}+24\hat{j}$
4. $-18\hat{i}-24\hat{j}$

Q. A constant force of $F=\frac{m_{2}g}{2}$ is applied on the block of mass $m_1$ as shown in figure. The string and the pulley are light and the surface of the table is smooth. The acceleration of $m_1$ is

1. $\frac{m_{2}g}{2(m_1+m_2)}$ towards right.
2. $\frac{m_{2}g}{2(m_1-m_2)}$ towards left.
3. $\frac{m_{2}g}{2(m_2-m_1)}$ towards right.
4. $\frac{m_{2}g}{2(m_2-m_1)}$ towards left.

Q. A block of mass $2\text{kg}$ slides down an incline plane of inclination ${30}^{\circ }$. The coefficient of friction between block and plane is $0.5$. The contact force between block and incline plane is :

1. $25N$
2. $10\sqrt{3}N$
3. $5\sqrt{7}N$
4. $5\sqrt{15}N$

Q. Two blocks $A$ and $B$ of mass $M$ and $2M$ respectively, are hanging from a ceiling by means of a massless spring and a light string as shown. If the string between the blocks is suddenly cut and the downward acceleration is taken positive, then what will be the acceleration of the block $A$ and $B$?

1. $g,2g$
2. $2g,g$
3. $-2g,g$
4. $2g,-g$

Q. Two blocks ‘$A$’ and ‘$B$’ of same mass '$m$' connected by a light spring are suspended by a string as shown in figure. Find the acceleration of block ‘$A$’ and ‘$B$’ just after the string is cut.

1. $0,2g$
2. $0,0$
3. $g,g$
4. $2g,0$

Q. A person of mass $60\text{kg}$ is inside a lift of mass $940\text{kg}$ and presses the button on control panel. The lift starts moving upwards with an acceleration $1.0{\text{m/s}}^2$. If $g=10{\text{m/s}}^2$, the tension in the supporting cable is

1. $9680\text{N}$
2. $11000\text{N}$
3. $1200\text{N}$
4. $8600\text{N}$

Q. In the figure, all surfaces are smooth. Find the acceleration of the body and the force exerted by the floor on the body. (Take $g=10m/s^2$)

1. $0,100N$
2. $4m/s^2,200N$
3. $2m/s^2,210N$
4. $0,220N$

Q. Mr. $A,B\text{and}C$ are trying to put a heavy piston into a cylinder at a mechanical workshop in a railway yard. If they apply forces $F_1,F_2\text{and}{F}_3$ respectively on the ropes, then, what is the relation between the forces if piston decends vertically with uniform speed?

1. $\sqrt{3}{F}_1=F_2+2F_3$
2. $\sqrt{2}{F}_1=F_2+F_3$
3. $2F_2=\sqrt{3}{F}_1-\frac{F_3}{2}$
4. $F_3=2F_1-\sqrt{3}{F}_2$

Q. Find the reading of the spring balance if it is assumed to be of negligible mass.
(Take $g=10m/s^2$)

1. $2kg$
2. $2.4kg$
3. $3kg$
4. $2.5kg$

Q. In the figure below, if all the surfaces are assumed to be smooth and the force $F=100N$. If the acceleration of block $B$ of mass $20kg$ is $a$ and tension in string connecting block $A$ of mass $20kg$ is $T$ then, just after force $F$ is applied find the values of $T$ and $a$.

1. $T=0,$ and $a=5m/s^2$
2. $T=100N,$ and $a=0$
3. $T=200N,$ and $a=5m/s^2$
4. $T=100N,$ and $a=5m/s^2$

Q. A block of mass $2\text{kg}$ slides down an incline plane of inclination ${30}^{\circ }$. The coefficient of friction between block and plane is $0.5$. The contact force between block and incline plane is :

1. $25N$
2. $10\sqrt{3}N$
3. $5\sqrt{7}N$
4. $5\sqrt{15}N$

Q. Find the acceleration ( in ${\text{m/s}}^2$) of $2\text{kg}$ block in the figures $\left(A\right)$ and $\left(B\right)$ shown at the instant when $1\text{kg}$ block falls from $2\text{kg}$ block (at $t=0$). (Systems are in equilibrium at $t=0$)
(Take $g=10m/s^2$)

1. $0,0$
2. $0,5$
3. $5,5$
4. $5,0$

Q. A gun fires $20$ bullets/sec each of mass $20\text{gm}$, with a muzzle velocity of $50\text{m/s}$. Find the force required to hold the gun in position.

1. $20\text{N}$
2. $50\text{N}$
3. $8.67\text{N}$
4. $42.22\text{N}$

Q. Position of a $10\text{kg}$ block moving under influence of a force is given as $s=6t^3+5t^2+10\left(\text{m}\right)$, where $\text{t}$ is in seconds. Find out the force acting after $10sec$.

1. $5000\text{N}$
2. $4000\text{N}$
3. $3600\text{N}$
4. $3700\text{N}$

Q. Five persons $A,B,C,D$ and $E$ are pulling a cart of mass $100\text{kg}$ on a smooth surface and cart is moving with acceleration $3{\text{m/s}}^2$ in east direction. When person $A$ stops pulling, it moves with acceleration $1{\text{m/s}}^2$ in the west direction. When person $B$ stops pulling, it moves with acceleration $24{\text{m/s}}^2$ in the north direction. The magnitude of acceleration of the cart when only $A$ and $B$ pull the cart keeping their directions same as the old directions, is

1. $24{\text{m/s}}^2$
2. $3\sqrt{71}{\text{m/s}}^2$
3. $30{\text{m/s}}^2$
4. $25{\text{m/s}}^2$

Q. When forces $F_1,F_2,F_3$ are acting on a particle of mass $m$ such that $F_2$ and $F_3$ are mutually perpendicular, then the particle remains stationary. If the force $F_1$ is now removed then the magnitude of acceleration of the particle is

1. $\frac{F_1}{m}$
2. $\frac{F_2{F}_3}{m{F}_1}$
3. $\frac{(F_2-F_3)}{m}$
4. $\frac{F_2}{m}$

Q. Two blocks are connected by a string as shown in the diagram. The upper block is hung by another string. A force $F$ applied on the upper string produces an acceleration of $2{\text{m/s}}^2$ in the upward direction in both the blocks. If $T$ and $T^{\prime }$ be the tensions in the two parts of the string, then (take $g=10{\text{m/s}}^2$ )

1. $T=72\text{N}$ and $T^{\prime }=48\text{N}$
2. $T=48\text{N}$ and $T^{\prime }=72\text{N}$
3. $T=48\text{N}$ and $T^{\prime }=24\text{N}$
4. $T=24\text{N}$ and $T^{\prime }=48\text{N}$

Q. A block of mass $m=15\text{kg}$ is attached to a spring of stiffness $K=100\text{N/m}$. The block descends a plane inclined at an angle $\alpha ={30}^{\circ }$ with horizontal. Assuming there is no friction, determine the acceleration of the block when the spring has stretched by a length $x=0.05\text{m}$. (Acceleration due to gravity is $10{\text{m/s}}^2$)

Q. Why is the block at rest despite an external force because of the pushing guy?

1. Oh God, Newton's Laws are wrong, what should I do?
2. Friction force by the block on the guy
3. Friction force by the guy on the block
4. Friction force by the ground on the block

Q. A projectile of mass $0.5\text{kg}$ is thrown with a velocity of $30\text{m/s}$ at an angle of ${60}^{\circ }$ with the horizontal. Find the net force acting on the body when in air. (Take $g=9.8m/s^2$)

1. $9.8\text{N}$
2. $4.9\text{N}$
3. $14.4\text{N}$
4. $10\text{N}$

Q. A body of mass $5\text{kg}$ under the action of constant force $\overrightarrow{F}=F_x\hat{i}+F_y\hat{j}$ has velocity at $t=0\text{s}$ as $\overrightarrow{u}=(6\hat{i}-2\hat{j})\text{m/s}$ and at $t=10\text{s}$ as $\overrightarrow{v}=6\hat{j}\text{m/s}$. The force $F$ is

1. $(-3\hat{i}+4\hat{j})\text{N}$
2. $(-\frac{3}{5}\hat{i}+\frac{4}{5}\hat{j})\text{N}$
3. $(3\hat{i}-4\hat{j})\text{N}$
4. $(\frac{3}{5}\hat{i}-\frac{4}{5}\hat{j})\text{N}$