Pseudo Force

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 $m$ on it. The bead can slide on the wire without friction. It stays at the lowestpoint of the parabola when the wire is at rest. The wire is now accelerated parallel to the $x$-axis with a constant acceleration $a$. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire, from the $y$-axis is

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

Q. There is no friction anywhere in the system shown in figure. The pulley is light. The wedge is free to move on the frictionless surface. A horizontal force $F$ is applied on the system in such a way that $m$ does not slide on $M$ or both move together with some common acceleration. Given $M>\sqrt{2}m$.

Match the entries of Column I with that of Column II.

$\begin{array}{cc}\text{Column I}& \text{Column II}\\ \text{i.Pseudo-force acting on m as seen from the frame of M is}& \text{a. equal to}\frac{mF}{m+M}\\ \text{ii.Pseudo-force acting on M as seen from the frame of m is}& \text{b. greater than}\frac{mF}{m+M}\\ \text{iii. Normal force (for}\theta ={45}^{\circ })\text{between m and M is}& \text{c. less than}mg\sin \theta \\ \text{iv. Normal force between ground and M is}& \text{d. greater than}mg\sin \theta \end{array}$

1. $\text{i- a, c; ii- b, c; iii- b, c; iv- b, d}$
2. $\text{i- b, c; ii- a, c; iii- b, c; iv- b, d}$
3. $\text{i- b, c; ii- a, c; iii- b, d; iv- b, c}$
4. $\text{i- b, c; ii- b, d; iii- a, c; iv- b, c}$

Q. A bob of mass $m$ is suspended from a ceiling of a trolley by a light inextensible string. When the trolley accelerates horizontally, the string makes an angle $\theta$ with the vertical. Then choose the correct statement.

1. $\theta$ depends on the acceleration of trolley only
2. $\theta$ depends on the acceleration of trolley and acceleration due to gravity
3. $\theta$ depends on mass of bob, acceleration of trolley and acceleration due to gravity.
4. none of these

Q. With what minimum acceleration can a fireman slide down a rope whose breaking strength is $\frac{2}{3}$ of his weight?
(Hint:-Use the concept of pseudo-force.)

1. $\frac{2g}{3}$
2. $g$
3. $\frac{g}{3}$
4. $\text{zero}$

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 the acceleration due to gravity) will be

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

Q.

A particle is observed from two frames $S_{1}and{S}_2$. The frame $S_2$ moves with respect to $S_1$ with an acceleration a. Let $F_{1}and{F}_2$ be the pseudo forces on the particle when seen from $S_{1}and{S}_2$ respectively. Which of the following are not possible?

1. $F_1=0,F_2\ne 0$

2. $F_1\ne 0,F_2=0$

3. $F_1\ne 0,F_2\ne 0$

4. $F_1=0,F_2=0$

Q.

A book is resting on the surface of a table. Consider the following four forces that arise in this situation.

1. The force of the earth pulling on the book.
2. The force of the table pushing on the book.
3. The force of the book pushing on the table.
4. The force of the book pulling on the earth.

Based on the above information, answer the following questions:

Which two forces form an action-reaction pair?

1. $1and2$
2. $1and3$
3. $1and4$
4. $2and4$

Q. The reading of the spring balance for the system shown in the figure is (in $kg$). The elevator is going up with an acceleration of $\frac{g}{10}{\text{m/s}}^2$.
(Take $g=10{\text{m/s}}^2$)

Q.

Why do we do Dot Product?

Q. A rail-road car is moving towards the right with acceleration $a$ and a dog of mass $m$ is chasing a man $\left(A\right)$ with an acceleration $\frac{a}{3}$ relative to the car and the man $\left(A\right)$ is accelerating towards left with an acceleration of magnitude $\frac{a}{3}$ with respect to the car as shown in the figure. If an observer $B$ on the ground is observing both the dog and man $\left(A\right)$, then the net force experienced by the dog as seen by observer $B$ is

1. $\frac{ma}{3}\hat{i}$
2. $\frac{-ma}{3}\hat{i}$
3. $\frac{-2ma}{3}\hat{i}$
4. $\frac{2ma}{3}\hat{i}$

Q. A simple pendulum is suspended to roof of a car. The car is moved with uniform velocity ${}^{\prime }{v}^{\prime }$. If the string makes an angle ${}^{\prime }{\theta }^{\prime }$ with vertical, ${}^{\prime }{\theta }^{\prime }$ will be equal to :

1. $\frac{v}{g}$
2. $\frac{v^2}{g}$
3. $vg$
4. $\text{Zero}$

Q. A downward force of $100\text{N}$ is applied to the small piston with a diameter of $50\text{cm}$ in the hydraulic lift system as shown in figure. What will be the upward force exerted on the large position with a diameter of $1\text{m}$?

1. $300\text{N}$
2. $50\text{N}$
3. $400\text{N}$
4. $600\text{N}$

Q. A bob of mass ${}^{\prime }{m}^{\prime }$ is attached to ceiling of a lift with the help of string as shown. Calculate tension in string when lift is accelerated up with acceleration ${}^{\prime }{a}^{\prime }$.

1. $m(g+a)$
2. $m(g-a)$
3. $m\sqrt{g^2+a^2}$
4. $mg$

Q. A downward force of $100\text{N}$ is applied to the small piston with a diameter of $50\text{cm}$ in the hydraulic lift system as shown in figure. What will be the upward force exerted on the large position with a diameter of $1\text{m}$?

1. $300\text{N}$
2. $50\text{N}$
3. $400\text{N}$
4. $600\text{N}$

Q. A small metallic sphere of mass $m$ is suspended from the ceiling of a car accelerating on a horizontal road with constant acceleration $a$ as shown in the figure. The tension in the string attached with the metallic sphere is

1. $mg$
2. $m(g+a)$
3. $m(g-a)$
4. $m\sqrt{g^2+a^2}$

Q. The block of mass $2\text{kg}$ is in equilibrium w.r.t $8\text{kg}$ wedge. The wedge is pushed by a force of $F=5\text{N}$ in $+x$ direction as shown. Find the pseudo force acting on a block of mass $m=2kg$.

1. $1\text{N},-x$ direction
2. $2\text{N},-x$ direction
3. $1\text{N},+x$ direction
4. $2\text{N},+x$ direction

Q. With what acceleration ${}^{\prime }{a}^{\prime }$ shown, the elevator descends so that the block of mass $M$ exerts a force of $\frac{Mg}{10}$ on the weighing machine? [$g$ = acceleration due to gravity]

1. $0.3g$
2. $0.1g$
3. $0.9g$
4. $0.6g$

Q. A block is placed on an inclined plane moving horizontally towards right with an acceleration $a=g$. Take $g=10{\text{ms}}^{-2}$ .The length of plane $\text{AC}=1\text{m}$. Friction is absent everywhere. Time taken by the block to reach from $\text{C}$ to $\text{A}$ is

1. $0.5\text{s}$
2. $1\text{s}$
3. $\sqrt{2}\text{s}$
4. $2\text{s}$

Q. A man of mass $m$ slides down along a rope that is connected to the ceiling of an elevator with deceleration $a$ relative to the rope. If the elevator is going upward with an acceleration $a$ relative to the ground, then tension in the rope is

1. $mg$
2. $m(g+2a)$
3. $m(g+a)$
4. zero

Q. With what acceleration $a$ should the bigger box shown in the figure descend so that the block of mass $M$ exerts a force $\frac{Mg}{4}$ on the floor of the box?
(Hint:- Use the concept of pseudo-force)

1. $g/4$
2. $g/2$
3. $3g/4$
4. $4g$

Q. A trolley ($100\text{kg}$) moving forward with acceleration of $1{\text{m/s}}^2$ has block of $1\text{kg}$ mass present on its floor. Find pseudo force acting on block ${}^{\prime }{A}^{\prime }$ with respect to a reference frame attached to trolley

1. $-1\text{N}$
2. $1\text{N}$
3. $100\text{N}$
4. $10\text{N}$

Q. A pendulum of mass $m$ hangs from a support fixed to a trolley. The inclination of the string (i.e. angle $\theta$) when the trolley moves up a plane of inclination $\alpha$ with acceleration $a$ is-

1. Zero
2. ${\tan }^{-1}\alpha$
3. ${\tan }^{-1}\left(\frac{a+g\sin \theta }{g\cos \alpha }\right)$
4. ${\tan }^{-1}\left(\frac{a}{g}\right)$

Q. In the figure shown, the minimum value of the acceleration of wedge ($a$) at which the cylinder starts rising up the inclined surface is

1. $g\tan \theta$
2. $g\cot \theta$
3. $g\sin \theta$
4. $g\cos \theta$

Q. Three forces, each of magnitude F, are applied on the disc of mass m and radius R lying in the x-y plane as shown in the figure. The net torque on the disc about the centre of the disc will be (All the forces are in the plane of disc)

चित्र में दर्शाए अनुसार x-y तल में स्थित m द्रव्यमान व R त्रिज्या की डिस्क पर समान परिमाण F के तीन बल आरोपित किए जाते हैं। डिस्क के केन्द्र के सापेक्ष डिस्क पर नेट बल आघूर्ण होगा (सभी बल डिस्क के तल में हैं)

1. $FR\hat{k}$
2. $\frac{5FR}{2}\hat{k}$
3. $\frac{3FR}{2}\hat{k}$
4. Zero (शून्य)

Q. A passenger is travelling inside a train moving at $40m{s}^{-1}$. His suitcase is kept on the berth. The driver of train applies breaks such that the speed of the train decreases at a constant rate to $20m{s}^{-1}$ in $4s$. What should be the minimum coefficient of friction between the suitcase and the berth if the suitcase is not to slide during retardation of the train? (Take $g=10m/s^2$)

1. $0.3$
2. $0.5$
3. $0.1$
4. $0.2$

Q. A spring balance attached to the roof of a moving elevator indicates $80\text{kg}$ weight as the weight of a $120\text{kg}$ body. What is the acceleration of the elevation? (Take $g=10m/s^2$)

1. $9.8{\text{m/s}}^2$
2. $4.9{\text{m/s}}^2$
3. $2{\text{m/s}}^2$
4. $3.3{\text{m/s}}^2$

Q. A block of mass m is placed on a wedge. The wedge can be accelerated in four manners marked as (1), (2), (3) and (4) as shown. If the normal reactions in situation (1), (2), (3) and (4) are $N_1,N_2,N_{3}and{N}_4$ respectively and acceleration with which the block slides on the wedge in situations are $b_1,b_2,b_{3}and{b}_4$ respectively then:

1. $N_3>N_1>N_2>N_4$
2. $N_4>N_3>N_1>N_2$
3. $b_2>b_3>b_4>b_1$
4. $b_2>b_3>b_1>b_4$

Q. A block is sliding along incline as shown in the figure. If the acceleration of the chamber is $a$ as shown in the figure. The time required to cover a distance $L$ along the incline is:

1. $\sqrt{\frac{2L}{g\sin \theta -a\cos \theta }}$
2. $\sqrt{\frac{2L}{g\sin \theta +a\sin \theta }}$
3. $\sqrt{\frac{2L}{g\sin \theta +a\cos \theta }}$
4. $\sqrt{\frac{2L}{g\sin \theta }}$

Q. The tension in the inextensible string using pseudo-force concept is (in N) (Take $g=10m/s^2$)

Q. A car has two travellers of masses $m_1$ and $m_2$. If the car moves towards east with acceleration ${}^{\prime }{a}^{\prime }$, find pseudo force on $m_1$ as observed by traveller of mass $m_2$

1. $m_{1}a\left(\text{West}\right)$
2. $m_{1}a\left(\text{East}\right)$
3. $m_{2}a\left(\text{West}\right)$
4. $m_{2}a\left(\text{East}\right)$