Net Force

Q. Two free point charges +4Q and +Q are placed at a distance r. A third charge q is so placed such that all the three are in equilibrium.

1. q is placed at a distance $\frac{1}{3}r$ from 4Q
2. $q=\frac{4Q}{9}$
3. q is placed at a distance $\frac{1}{2}r$ from Q
4. $q=-\frac{4Q}{9}$

Q. In which all cases should we take gravitational acceleration 'g' as negative and where should we take it as positive?

Q. Four charges $q_1=1\mu \text{C}$, $q_2=2\mu \text{C}$, $q_3=-3\mu \text{C}$ and $q_4=4\mu \text{C}$ are kept on the vertices of a square of side $1\text{m}$. Find the electric potential energy stored in this system of charges.

1. $3.6\times {10}^{-2}\text{J}$
2. $-7.62\times {10}^{-2}\text{J}$
3. $7.62\times {10}^{-2}\text{J}$
4. $-3.6\times {10}^{-2}\text{J}$

Q.

If the resultant of two forces of magnitudes $P$ and $Q$ acting at a point at an angle of $60°$ is $\sqrt{7}Q$, then $\frac{P}{Q}$ is

1. $1$

2. $\frac{3}{2}$

3. $2$

4. $4$

Q.

The moment of inertia of thin disc of mass $m$ and radius $r$, about an axis passing through one of its diameter is given by

Q. What is force constant?

Q. Two blocks A and B of masses $2m$ and $m$ respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in the figure. The magnitudes of acceleration of A and B, immediately after the string is cut, are respectively:

1. $g,\frac{g}{2}$
2. $\frac{g}{2},g$
3. $g,g$
4. $\frac{g}{2},\frac{g}{2}$

Q.

Find the torque about the origin when a force of $3\hat{j}N$ acts on a particle whose position vector is $2\hat{k}N$ m.

Q.

If the resultant of two forces of magnitude P and 2P is perpendicular to P, then the angle between the forces is

1. $2\pi /3$

2. $3\pi /4$

3. $4\pi /5$

4. $5\pi /6$

Q. A system of three charges are placed as shown in the figure.


If $D>>d$, the potential energy of the system is best given by

1. $\frac{1}{4\pi {ϵ}_0}[\frac{-q^2}{d}-\frac{qQd}{2D^2}]$
2. $\frac{1}{4\pi {ϵ}_0}[-\frac{q^2}{d}-\frac{qQd}{D^2}]$
3. $\frac{1}{4\pi {ϵ}_0}[+\frac{q^2}{d}+\frac{qQd}{D^2}]$
4. $\frac{1}{4\pi {ϵ}_0}[\frac{-q^2}{d}+\frac{2qQd}{D^2}]$

Q. A particle is simultaneously acted upon by two forces of magnitudes $4N$ and $3N$. The net force on the particle is

1. $7N$
2. $5N$
3. $1N$
4. Between $1N$ snd $7N$.

Q. A block of mass $m$ is connected to another block of mass $M$ by a massless spring of spring constant $k$. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force $F$ starts acting on the block of mass $M$ to accelerate it. Find the force on the block of mass $m$.

1. $\frac{MF}{(m+M)}$
2. $\frac{MF}{m}$
3. $\frac{(M+m)F}{m}$
4. $\frac{mF}{m+M}$

Q. A block of mass $0.1\text{kg}$ is held against a wall by applying a horizontal force of $5\text{N}$ on the block. If the coefficient of friction between the block and the wall is $0.5$, the magnitude of the friction force acting on the block is

1. $0.49\text{N}$
2. $2.5\text{N}$
3. $0.98\text{N}$
4. $4.9\text{N}$

Q.

Two forces equal to P and 2P newton act on a particle. If the first be doubled and the second be incresed by 20N , the direction of the resultant is unaltered. Find the value of P.

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. $8600\text{N}$
4. $1200\text{N}$

Q.

What is the unit of moment of force?

Q. In the following options you are given the magnitudes of three forces in Newton acting simultaneously on a body. Find the set for which the resultant force on the body can be zero.

1. $10,20,35$
2. $15,30,14$
3. $10,8,2$
4. $40,19,17$

Q. Two point charges $Q$ and $-\frac{Q}{4}$ placed along the $\text{x-}$axis are separated by a distance $r$. Take $-\frac{Q}{4}$ as origin and it is placed to the right of $Q$. Then the potential is zero

1. at $x=\frac{r}{4}$ only
2. at $x=-\frac{r}{5}$ only
3. both at $x=\frac{r}{3}$ and at $x=-\frac{r}{5}$
4. there exist two points on the axis, where the electric field is zero.

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. A bullet of $4\text{g}$ mass is fired from a gun of mass $4\text{kg}$. If the bullet moves with the muzzle speed of $50{\text{ms}}^{–1}$, the impulse imparted to the gun and velocity of recoil of gun are :

1. $0.4{\text{kg ms}}^{-1},0.05{\text{ms}}^{-1}$
2. $0.4{\text{kg ms}}^{-1},0.1{\text{ms}}^{-1}$
3. $0.2{\text{kg ms}}^{-1},0.1{\text{ms}}^{-1}$
4. $0.2{\text{kg ms}}^{-1},0.05{\text{ms}}^{-1}$

Q. Action and reaction can never balance out because

1. they are equal but not opposite always.
2. they are unequal in magnitude even though opposite in direction.
3. though they are equal in magnitude and opposite in direction they act on different bodies.
4. they are unequal in magnitudes.

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 trolley filled with sand is moving with a velocity of $v$ on a smooth horizontal surface. If the sand starts falling off at the rate of $\mu \text{kg/s}$ from the hole at its bottom, the velocity$\left(v\right)$ of the trolley as a function of time$\left(t\right)$ will be best represented by -

1. 
2. 
3. 
4. 

Q.

What do you understand by the term dynamics?

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

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

Q. A bar of uniform cross-section and having a length $l$ is hanging from the roof. What will be the elongation in bar due to self weight if $\gamma$ is the specific weight of the bar and $Y$ is the young's modulus of elasticity?

1. $\frac{\gamma l^2}{Y}$
2. $\frac{\gamma l}{2Y}$
3. $\frac{\gamma l^3}{Y}$
4. $\frac{\gamma l^2}{2Y}$

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

Q.

A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble,
a) during its upward motion,
b) during its downward motion,
c) at the highest point where it is momentarily at rest. Do your answers change if the pebble was thrown at an angle of ${45}^{\circ }$ with the horizontal direction?
Ignore air resistance.

Q. A rod of mass $m$ and length $2R$ is attached to a circular ring of mass $mandradiusR$ along its vertical diameter as shown. Horizontal force $F$ is applied at top. Friction is sufficient for pure rolling, then friction force acting on the ring, at the instant shown is

1. $\frac{F}{2}$
2. $\frac{F}{5}$
3. $\frac{2F}{3}$
4. $\frac{F}{7}$