Problems with Pseudo Force

Q. What will be the reading of spring balance shown in the figure, if it is moving in upward direction with a constant acceleration $a=2{\text{m/s}}^2$ and an initial velocity $v=2\text{m/s}$. (Take $g=10{\text{m/s}}^2$)

1. $80\text{N}$
2. $100\text{N}$
3. $120\text{N}$
4. $140\text{N}$

Q. In the system shown in figure, masses of the blocks are such that when system is released, acceleration of pulley $P_1$ is $a$ upwards and acceleration of block 1 is $a_1$ upwards, such that $a<a_1<2a$.
It is found that acceleration of block 3 is same as that of 1 both in magnitude and direction.

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{a) Acceleration of}2& p)2a+a_1\\ \text{b) Acceleration of}4& q)2a-a_1\\ \text{c) Acceleration of}2\text{w.r.t.}3& \text{r) upwards}\\ \text{d) Acceleration of}2\text{w.r.t.}4& \text{s) downwards}\end{array}$

1. $a-(q,r)b-(p,s)c-\left(s\right)d-\left(r\right)$
2. $a-\left(r\right)b-\left(r\right)c-\left(s\right)d-\left(r\right)$
3. $a-\left(q\right)b-(p,r)c-\left(s\right)d-\left(r\right)$
4. $a-(q,r)b-(p,s)c-(s,r)d-(r,s)$

Q. In the arrangement shown in the figure, mass of the block $B$ and $A$ are $2m$, $8m$ respectively. Surface between $B$ and the floor is smooth. The block $B$ is connected to block $C$ by means of a pulley. If the whole system is released from rest, then find the minimum value of mass of block $C$ so that the block $A$ remains stationary with respect to $B$. Given coefficient of static friction between $A$ and $B$ is $\mu$ and pulley is ideal.

1. $\frac{m}{\mu }$
2. $\frac{2m}{\mu +1}$
3. $\frac{10m}{\mu }$
4. $\frac{10m}{\mu -1}$

Q. A block of mass $m=2\text{kg}$ is placed on an inclined surface, which is placed inside a truck as shown in the figure. The coefficient of static friction ($\mu$) between the block and the inclined plane is $0.25$. If the truck accelerates at the rate of $2{\text{m/s}}^2$, what should be the maximum angle of the inclined surface so that the block does not slide down the incline? Take $g=10{\text{m/s}}^2$ .

1. ${\tan }^{-1}\left(0.047\right)$
   
2. ${\tan }^{-1}\left(7.47\right)$
   
3. ${\tan }^{-1}\left(0.07\right)$
   
4. ${\tan }^{-1}\left(0.56\right)$
   

Q. A cart of mass $M$ moves with acceleration $a$ as shown in the figure. The minimum force required to hold a block of mass $m$ together is $($friction coefficient between two blocks is $\mu )$

1. $\frac{(M-m)g}{\mu }$
2. $\frac{(M+m)g}{\mu }$
3. $\frac{Mg}{\mu }$
4. $\frac{mg}{\mu }$

Q. In the arrangement shown in the figure, masses of the blocks $A$ and $B$ are $\text{m}$ and $2\text{m}$ respectively. Surface between block $B$ and floor is smooth. The block $B$ is connected to the block $C$ by means of a string pulley system. If the whole system is released, then find the minimum value of mass of block $C$ so that block $A$ remains stationary w.r.t. $B$. Coefficient of friction between $A$ and $B$ is $\mu$.

1. $\frac{m}{\mu }$
2. $\frac{2m+1}{\mu +1}$
3. $\frac{3m}{\mu -1}$
4. $\frac{6m}{\mu +1}$

Q. A light and smooth pulley is attached to the ceiling of a lift moving upward with acceleration $a_0=2{\text{m/s}}^2$ as shown in the figure. Two blocks of equal masses $(m=3\text{kg})$ are attached to the two ends of a massless string passing over the pulley. Find the tension in the string. (Take $g=10{\text{m/s}}^2$).

1. $12\text{N}$
2. $24\text{N}$
3. $10\text{N}$
4. $36\text{N}$

Q. Find the force exerted by $5\text{kg}$ block on floor of lift, as shown in figure. (Take $g=10m/s^2)$

1. 100 N
2. 115 N
3. 105 N
4. 135 N

Q. A block of mass $m$ is kept on an inclined plane inside a lift moving down with acceleration of $2{\text{m/s}}^2$. What should be the coefficient of friction between block and inclined plane to let the block move down with constant velocity relative to lift?
(Take $g=10{\text{m/s}}^2$)

1. $\frac{1}{\sqrt{3}}$
2. $\frac{1}{\sqrt{5}}$
3. $\frac{1}{\sqrt{6}}$
4. $\frac{1}{\sqrt{2}}$

Q. A pulley system is attached to an elevator as shown in figure. The elevator starts to move up with an acceleration $a$.

Match statements in column I with results in column II.
$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{(a)}& \text{Acceleration of}{m}_1\text{in elevator frame}& \text{(p)}& \frac{1}{2}\left(\frac{(m_2-m_1)g+2m_{2}a}{m_1+m_2}\right)t^2\\ \text{(b)}& \text{Acceleration of}{m}_1\text{in ground frame}& \text{(q)}& \frac{1}{2}\left[\frac{m_2-m_1}{(m_1+m_2)}\right(g+a\left)\right]t^2\\ \text{(c)}& \text{Distance covered of}{m}_1\text{in elevator frame}& \text{(r)}& \left(\frac{m_2-m_1}{m_1+m_2}\right)g+\left(\frac{2m_2}{m_1+m_2}\right)a\\ \text{(d)}& \text{Distance covered of}{m}_1\text{in ground frame}& \text{(s)}& \frac{(m_2-m_1)}{(m_1+m_2)}(g+a)\\ & & \text{(t)}& \text{None of the above}\end{array}$

1. a - s; b - r; c - q; d - p
2. a - r; b - q; c - p; d - s
3. a - s; b - t; c - q; d - t
4. a - r; b - q; c - s; d - p

Q. A block of mass m is placed on a smooth wedge of inclination $\theta$. The whole system is accelerated horizontally, so that the block does not slip on the wedge. The force exerted by the wedge on the block ($g$ is acceleration due to gravity) will be:

1. $mg\sin \theta$
2. $\text{mg}$
3. $\frac{mg}{\cos \theta }$
4. $mg\cos \theta$

Q.

A cylindrical vessel partially filled with water is rotated about its vertical central axis. It’s surface will

1. Rise equally

2. Rise from the sides

3. Rise from the middle

4. Lowered equally

Q. The rear side of a truck is open and a box of mass $20\text{kg}$ is placed on the truck $4\text{m}$ away from the open end. The coefficient of friction between the box and the surface is $0.15$. The truck starts from rest with an acceleration of $2{\text{m s}}^{-2}$ on a straight road. The box will fall off the truck when it is at a distance from the starting point equal to (take $g=10m{s}^{-2}$)

1. $4\text{m}$
2. $8\text{m}$
3. $16\text{m}$
4. $32\text{m}$

Q. If the coefficient of friction between $A$ and $B$ is $\mu$, the minimum horizontal acceleration of the wedge $A$ for which $B$ will remain at rest w.r.t. the wedge is

1. $\mu g$
2. $g\left(\frac{1+\mu }{1-\mu }\right)$
3. $\frac{g}{\mu }$
4. $g\left(\frac{1-\mu }{1+\mu }\right)$

Q. A trolley carries a body of weight $25kg$. which is kept at a distance of $2.5m$ from the rear end of the trolley. The trolley starts from rest and accelerates at a constant rate of $2m{s}^{-2}$ If the coefficient of friction between the trolley and the body is $0.1$, find the distance of the trolley from the starting point where the body will just slip out of the trolley. $\text{Take}g=10m{s}^{-2}$

1. $4m$
2. $3m$
3. $5m$
4. $10m$

Q. As shown in the figure, a truck has its rear side open and a box of $40\text{kg}$ mass is placed $5\text{m}$ away from the open end. The coefficient of friction between the box and the surface below it is $0.15$. On a straight road, the truck starts from rest and accelerates with $2{\text{m/s}}^2$. Find the distance (in metres) travelled by the truck by the time the box falls from the truck. (Ignore the size of the box). [Take $g=10{\text{m/s}}^2$]

1. $10\text{m}$
2. $5\text{m}$
3. $20\text{m}$
4. $15\text{m}$

Q. In the given figure, masses of $A$ and $B$ are $5\text{kg}$ and $10\text{kg}$ respectively. Coefficient of friction between blocks is 0.2. If the lower block is pulled rightwards with a constant force, $F=50\text{N}$, time elapsed before block $A$ falls off block $B$ is: (There is no friction between block $B$ and surface) and neglect the size of $A$)

1. $2s$
2. $\frac{3}{\sqrt{2}}s$
3. $\frac{2}{\sqrt{3}}s$
4. $\sqrt{\frac{3}{2}}s$

Q. In the arrangement shown in the figure, mass of the block $B$ and $A$ are $2m$, $8m$ respectively. Surface between $B$ and the floor is smooth. The block $B$ is connected to block $C$ by means of a pulley. If the whole system is released from rest, then find the minimum value of mass of block $C$ so that the block $A$ remains stationary with respect to $B$. Given coefficient of static friction between $A$ and $B$ is $\mu$ and pulley is ideal.

1. $\frac{m}{\mu }$
2. $\frac{2m}{\mu +1}$
3. $\frac{10m}{\mu }$
4. $\frac{10m}{\mu -1}$