Pendulum in Non Inertial Frame

Q. A simple pendulum has time period $T_1.$ The point of suspension is now moved upward according to the relation $y=k{t}^2,$ where $y$ is the vertical displacement and $k=1{\text{ms}}^{-2}$. The time period now becomes $T_2$. The ratio $\frac{T_1^2}{T_2^2}$ is equal to
$(g=10{\text{ms}}^{-2})$

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

Q.

Two masses A and B, each of mass M are fixed together by a massless spring. A force acts on mass B as shown in the figure. If mass A starts moving away from mass B with acceleration ‘a’, then the acceleration of mass B will be:

1. $\frac{\left(F+\hspace{0.17em}Ma\right)}{M}$

2. $\frac{\left(F-Ma\right)}{M}$

3. $\frac{\left(Ma-F\right)}{M}$

4. $\frac{MF}{\left(F+Ma\right)}$

Q.

In figure shows a man of mass 60 kg standing on a light weighing machine kept in a box of mass 30 kg. The box is hanging from a pulley fixed to the ceiling through a light rope, the other end of which is held by the man himself. If the man manages to keep the box at rest, what is the weight shown by the machine ? What force should he exert on the rope to get his correct weight on the machine ?

Q.

The time period of a simple pendulum, whose bob is a hollow metallic sphere is T. Time period is $T_1$ when the bob is filled with sand, $T_2$ when it is filled with mercury, and $T_3$ when it is half-filled with mercury. Which of the following is true?

1. T=$T_1$ =$T_2$ >$T_3$
2. $T_1$ =$T_2$ =$T_3$ >T
3. T>$T_3$ >$T_1$ =$T_2$
4. T=$T_1$ =$T_2$ <$T_3$

Q. A small steel ball of radius $r$ is allowed to fall under gravity through a column of a viscous liquid of coefficient of viscosity $\eta$. After some time the velocity of the ball attains a constant value known as terminal velocity $v_T.$ The terminal velocity depends on $\left(i\right)$ the mass of the ball $m$, $\left(ii\right)$ $\eta$, $\left(iii\right)$ $r$, and $\left(iv\right)$ acceleration due to gravity $g$. Which of the following relations is dimensionally correct?

1. $v_T\propto \frac{mg}{\eta r}$
2. $v_T\propto \frac{\eta r}{mg}$
3. $v_T\propto \eta rmg$
4. $v_T\propto \frac{mgr}{\eta }$

Q. A simple pendulum of length $l$ having a bob of mass $m$ is suspended in a car that is travelling with a constant speed $v$ around a circular path of radius $R$. If the pendulum undergoes small oscillations about its equilibrium position, the frequency of its oscillation will be

1. $\frac{1}{2\pi }\sqrt{\frac{g}{l}}$
2. $\frac{1}{2\pi }\sqrt{\frac{{(g^2+\frac{v^4}{R^2})}^{\frac{1}{2}}}{l}}$
3. $\frac{1}{2\pi }\sqrt{\frac{g}{R}}$
4. $\frac{1}{2\pi }\sqrt{\frac{v^2}{Rl}}$

Q. Figure shows two block system, 4 kg block rests on a smooth horizontal surface, upper surface of 4 kg is rough a block of mass 2 kg is placed on its upper surface the acceleration of a upper blockwith respect to earth when 4 kg mass is pulled by a force of 30 newborn, is 1)6m/s 2)5 m/s 3)8m/s 4)2m/s

Q.

The acceleration due to gravity on the surface of moon is 1.7 ms^–2. What is the time period of a simple pendulum on the surface of moon if its time period on the surface of earth is 3.5 s? (g on the surface of earth is 9.8 ms^–2)

Q.

A simple pendulum is suspended from the ceiling of a car accelerating uniformly on a horizontal road. If the acceleration is $a_0$ and the length of the pendulum is l, find the time period of small oscillations about the mean position.

1. 

2. g+a

3. Particle won't oscillate with fixed time period

4. 

Q.

A particle of mass is fixed to one end of a light spring having force constant $k$ and unstretched length $l$. The other end is fixed. The system is given an angular speed about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is

1. $\frac{m{\omega }^{2}l}{k-m{\omega }^2}$

2. $\frac{m{\omega }^{2}l}{k+m{\omega }^2}$

3. $\frac{m{\omega }^{2}l}{k-m\omega }$

4. $\frac{m{\omega }^{2}l}{k+m\omega }$

Q.

Amplitude of a mass spring system, which is executing simple harmonic motion decreases with time. If $mass=500g$, $Decaycons\tan t=20g/s$ then how much time is required for the amplitude of the system to drop to half of its initial value?

1. $15.01s$

2. $17.32s$

3. $0.034s$

4. $34.65s$

Q. A simple pendulum is oscillating without damping. When the bob is at extreme position, acceleration vector is correctly shown by

1. 
2. 
3. 
4. 

Q. A block of mass 4 kg is placed on another block B of mass 5kg and the block B rests on smooth horizontal table. If the maximum force that can be applied on A so that both the blocks move together is 12N , the maximum force that can be applied on B for the blocks to move together will be

Q. The time period of a simple pendulum inside a stationary lift is $\sqrt{3}\text{s}$. When the lift moves downward with an acceleration $\frac{g}{4}$, find the time period of simple pendulum.

1. $1\text{s}$
2. $2\text{s}$
3. $6\text{s}$
4. $3\text{s}$

Q. A man measures the time period of a simple pendulum inside a stationary lift and finds it to be $10\text{sec}$. If the lift accelerates upwards with an acceleration $\frac{g}{4}$, then find the time period of the pendulum.

1. $8\sqrt{5}\text{sec}$
2. $4\sqrt{5}\text{sec}$
3. $2\sqrt{5}\text{sec}$
4. $10\sqrt{5}\text{sec}$

Q.

A simple pendulum hanging from the ceiling of a stationary lift has a time period $T_1$. When the lift moves downward with constant velocity, the time period is $T_2$, then

1. T₂ is infinity

2. T₂> T₁

3. T₂< T₁

4. T₂ = T₁

Q. A simple pendulum consists of a bob of mass $m$ and a light string of length $l$ as shown in the figure. Another identical ball moving with a small velocity $v_0$ collides with the pendulum's bob and sticks to it. For this new pendulum of mass $2m$, which of the following statement(s) is/are correct ?

1. Time period of the pendulum is $2\pi \sqrt{\frac{l}{g}}$.
2. The equation of motion for this pendulum is $\theta =\frac{v_0}{2\sqrt{gL}}\sin \left[\sqrt{\frac{g}{l}}t\right]$.
3. The equation of motion for this pendulum is $\theta =\frac{v_0}{4\sqrt{gl}}\cos \left[\sqrt{\frac{g}{l}}t\right]$.
4. Time period of the pendulum is $2\pi \sqrt{\frac{2l}{g}}$.

Q.

Figure shows a light rod of length l rigidly attached to a small heavy block at one end and a hook at the other end. The system is released from rest with the rod in a horizontal position. There is a fixed smooth ring at a depth h below the initial position of the hook and the hook gets into the ring as it reaches there. What should be the minimum value of h so that the block moves in a complete circle about the ring?

1. h = l

2. h = 3l

3. h = 4l

4. h = 2l

Q.

Answer the following questions:

(a) Time period of a particle in SHM depends on the force constant k and mass m of the particle:

. A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum?

(b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that T is greater than. Think of a qualitative argument to appreciate this result.

(c) A man with a wristwatch on his hand falls from the top of a tower. Does the watch give correct time during the free fall?

(d) What is the frequency of oscillation of a simple pendulum mounted in a cabinthat is freely falling under gravity?

Q. Three equal point masses of 1.5kg each are fixed at the vertices of equilateral triangle of side 1 m. What is the force acting on a particle of mass 1 kg place at its centroid

Q. The time period of the simple pendulum kept in a lift decreases when the lift is .

1. going up
2. going down
3. stationary

Q. A cart is falling freely under gravity. Find the time period of a simple pendulum attached to its ceiling.

1. $1\text{s}$
2. $2\text{s}$
3. $\infty$
4. $\text{Zero}$

Q. A simple pendulum of length 1 m is taken to height h (h = R = radius of the earth) from the earth’s surface.
The time period of small oscillation of the pendulum at that point is $(g={\pi }^{2}m{s}^{-2})$

1. 2 s
2. 3 s
3. 4 s
4. 1 s

Q. a ball of mass0.2kg strikes an obstacle and moves at 60 degree to its original direction. if its speed also changes from 20m/s to 10m/s, the magnitude of the impulse by the ball is

Q. An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is?

1. $10$ times greater
2. Equal
3. Smaller
4. $5$ times greater

Q.

Time period of a simple pendulum varies __________ as the square root of the length of the pendulum.

Q. A simple pendulum of length $100\text{cm}$ is suspended from the ceiling of a cart which is sliding without friction on an inclined plane of inclination ${60}^{\circ }$. Find the time period of the pendulum.
Take $g=10{\text{m/s}}^2$.

1. $2\text{s}$
2. $2.8\text{s}$
3. $5\text{s}$
4. $2.14\text{s}$

Q. A uniform rod of length $l$ and mass $m$ is fixed at the centre. A spring of spring constant $k$ is connected to rod and wall as shown in the figure. The rod is displaced by small angle $\theta$ and released. Find time period of oscillation.

1. $2\pi \sqrt{\frac{m}{k}}$
2. $2\pi \sqrt{\frac{m}{2k}}$
3. $2\pi \sqrt{\frac{3m}{k}}$
4. $2\pi \sqrt{\frac{m}{3k}}$

Q. The acceleration due to gravity is nearly 9.8 m/s^2. What is the order of magnitude of acceleration due to gravity in cgs unit?

Q. A simple pendulum is suspended from the roof of a trolley which moves, in a horizontal direction with an acceleration $a$, and its time period is given by $T=2\pi \sqrt{\frac{l}{g^{\prime }}}$ which of the following correctly represent the value of $g^{\prime }$.

1. $g$
2. $\sqrt{g^2+a^2}$
3. $g-a$
4. $g+a$