Problems with Pseudo Force

Q.

Find the reading of the spring balance shown in figure. The elevator is going up with an acceleration of g/10, the pulley and the string are light and the pulley is smooth.

1. 4.4 kg

2. 5 kg

3. 10 kg

4. 49.5 N

Q.

A box weighing $2000N$ is to be slowly slid through $20m$ on a straight track having friction coefficient $0.2$ with the box. Find the work done by the person pulling the box with a chain at an angle $\theta$ with the horizontal.

1. 

2. 8000 J

3. 

4. None of these

Q.

A wooden block is kept on a polished wooden plank and the inclination of the plank is gradually increased. It is found that the block starts slipping when the plank makes an angle of ${18}^{\circ }$ (angle of repose) with the horizontal. However, once the block starts slipping it can continue with uniform speed if the inclination is reduced to ${15}^{\circ }$. Find the coefficients of static and kinetic friction between the block and the plank.

1. = tan

   ⁼ tan

2. = tan ( + )

   ⁼ tan ( + )

3. = tan

   ⁼ tan

4. 

   =

Q. four point masses each of mass m are kept at the vertices of a square a point mass m is kept at the point of intersection of the diagonal of a square. what will be the force experienced by central mass m

Q. { A block of mass }15kg is held by a string on an inclined }}{ plane (angle }30^°). The tension }T in the string is }}{(g=10m/s^2)

Q.

A lift of mass 1000kg , which is moving with an acceleration of 1 m/s² in upward direction has tension developed in its string equal to:

1. 10000 N

2. 10800 N

3. 9800 N

4. 11000 N

Q. A light rope is passed over a pulley such that at its one end a block is attached, and on the other end a boy is climbing up with acceleration g/2 relative to slope. Mass of block is 30kg and that of boy is 40kg. find tension and acceleration of the rope.

Q. A solid cylinder of mass 50Kg and radius 0.5m is free to rotate about the horizontal axis a massless string is wound round the cylinder with one end attached to it and other hanging freely tension in the string required to produce an angular acceleration of 2rev/s^{2 is

Q. 19.An elevator accelerates upwards at a constant rate. A uniform string of length L and mass m supports a small black CK of mass M that hangs from the ceiling of the elevator. The tension at a distance l from the ceiling is T. Find the acceleration of the elevator.

Q. The string, the spring and the pulley shown in figure (12−E9) are light. Find the time period of the mass m.

Figure

Q. 24. A small metallic sphere of mass m is suspended from the ceiling of a car accelerating on a horizontal road with constant acceleration a. What will be the tension in the string attached with metallic sphere?

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 piece of wire is bent in the shape of a parabola $y=k{x}^2$ ($y$-axis vertical), with a bead of mass $m$ placed on it. The bead can slide on the wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the positive $x$-axis with a constant acceleration $a$. The distance of new equilibrium position of the bead from $y$-axis, where the bead can stay at rest with respect to the wire will be:

1. $\frac{a}{gk}$
   
2. $\frac{a}{2gk}$
   
3. $\frac{2a}{gk}$
   
4. $\frac{a}{4gk}$
   

Q. The monkey B, shown in the figure (5−E20), is holding on to the tail of monkey A that is climbing up a rope. The masses of monkeys A and B are 5 kg and 2 kg, respectively. If A can tolerate a tension of 30 N in its tail, what force should it apply on the rope in order to carry monkey B with it? Take g = 10 m/s².

Figure

Q. In a simple Atwood machine, two unequal masses m₁ and m₂ are connected by a string going over a clamped light smooth pulley. In a typical arrangement (figure 5−E7), m₁ = 300 g and m₂ = 600 g. The system is released from rest. (a) Find the distance travelled by the first block in the first two seconds; (b) find the tension in the string; (c) find the force exerted by the clamp on the pulley.

Figure

Q. A bob of mass m is suspended from the ceiling of a train moving with an acceleration a as shown in figure. Find the angle $\theta$ in equilibrium position.

1. ${\tan }^{-1}$ (a/g)

2. ${\cos }^{-1}$ (a/g)

3. ${\cot }^{-1}$ (a/g)

4. ${\sin }^{-1}$ (a/g)

Q. A person of mass $40\text{kg}$ is inside a lift of mass $960\text{kg}$ and presses the button on the control panel. The lift starts moving upwards with an acceleration $2{\text{m/s}}^2$. If $g=10{\text{m/s}}^2$, the tension in the supporting cable is

1. $8600\text{N}$
2. $12000\text{N}$
3. $11000\text{N}$
4. $2000\text{N}$

Q. A block of mass $M$ is placed on a rough floor of a lift. The coefficient of friction between the block and the floor is $\mu$. When the lift falls freely, the block is pulled horizontally on the floor. What will be the force of friction?

1. $\mu Mg$
2. $\frac{\mu Mg}{2}$
3. $2\mu Mg$
4. None of these

Q. 017. A ring of mass m (tree to rotate about its centre c)is wrapped by a thread which does not slip on thering. If the thread is pulled with an acceleration athen the tension in the string is

Q. In order to raise a mass of 100 kg, a man ofmass 60 kg fastens a rope to it and passesthere rope over a smooth pulley. He climbsthe rope with acceleration 5g/4 relative tothe rope. The tension is the rope is (take10 ms2)TIZELLТАAT

Q. A table with smooth horizontal surface is placed in a circle of a large radius R. A smooth pulley of small radius is fastened to the table. Two masses m and 2m placed on the table are connected through a string going over the pulley. Initially the masses are held by a person with the string along the outward radius and then the system is released from rest (with respect to the cabin). Find the magnitude of the initial acceleration of the masses as seen from the cabin and the tension in the string.
Figure

Q. A block is placed on the top of a smooth inclined plane of inclination $\theta$ kept on the floor of a lift. When the lift is descending with a retardation $a$, the block is released. The acceleration of the block relative to the incline is

1. $\text{g sin}\theta$
2. $\text{a sin}\theta$
3. $(g-a)\text{sin}\theta$
4. $(g+a)\text{sin}\theta$

Q. If the tension in the cable supporting an elevator is equal to the weight of the elevator, the elevator may be
(a) going up with increasing speed
(b) going down with increasing speed
(c) going up with uniform speed
(d) going down with uniform speed

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 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.

Two masses 8 kg and 12 kg are connected at the two ends of a light inextensible string that goes over a frictionless pulley. Find the acceleration of the masses, and the tension in the string when the masses are released.

Q. A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads $49\text{N}$, when the lift is stationary. If the lift moves downward with an acceleration of $5{\text{m/s}}^2$, the reading of the spring balance ( in $\text{N}$) will be

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. 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. The block of mass m₁ shown in figure (12−E2) is fastened to the spring and the block of mass m₂ is placed against it. (a) Find the compression of the spring in the equilibrium position. (b) The blocks are pushed a further distance (2/k) (m₁ + m₂)g sin θ against the spring and released. Find the position where the two blocks separate. (c) What is the common speed of blocks at the time of separation?

Figure