Spring Block's Time Period

Q.

What is the spring constant in parallel connection and series connection?

Q.

A spring of force constant $k$ is cut into lengths of ratio $1:2:3$. They are connected in series and the new force constant is $k$. They are connected in parallel and the force constant is $k"$. Then $k:k"$is:

Q.

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta T=0.01$ seconds and he measures the depth of the well to be $L=20$ meters. Take the acceleration due to gravity $g=10m{s}^{-2}$ and the velocity of sound is $300m{s}^{-1}$. Then the fractional error in the measurement, $\delta L/L$, is closest to

1. $2\%$

2. $5\%$

3. $1\%$

4. $3\%$

Q.

Does cutting a spring change the spring constant?

Q. Molten - wax of mass $m$ drops on a block of mass $M$, which is oscillating on a frictionless table as shown.
Select the incorrect option.

1. If the collision takes place at extreme position, time period increases
2. If the collision takes place at extreme position, amplitude does not change
3. If the collision takes place at mean position, amplitude decreases
4. If the collision takes place at mean position, time period decreases

Q. A block of mass $100\text{g}$ attached to a spring of spring constant $100{\text{Nm}}^{-1}$ is lying on a frictionless floor as shown. The block is moved to compress the spring by $10\text{cm}$ and then released. If the collisions with the wall in front are elastiac, then the time period of the motion is

1. $0.1\text{s}$
2. $0.5\text{s}$
3. $0.132\text{s}$
4. $0.2\text{s}$

Q. A spring having a spring constant $1200{\text{Nm}}^{-1}$ is mounted on a horizontal table as shown. A mass of $3.0\text{kg}$ is attached to the free end of the spring. The mass is then pulled sideways to a distance of $0.2\text{cm}$ and released. Determine
(i) The frequency of oscillations.
(ii) The maximum acceleration of the mass, and
(iii) the maximum speed of the mass?

1. $3.18\text{Hz},8{\text{m/s}}^2,0.40\text{m/s}$
2. $1.57\text{Hz},16{\text{m/s}}^2,0.80\text{m/s}$
3. $3.18\text{Hz},32{\text{m/s}}^2,1.6\text{m/s}$.
4. $3.18\text{Hz},16{\text{m/s}}^2,0.80\text{m/s}$

Q.

A heavy uniform chain lies on a horizontal tabletop. If the coefficient of friction between the chain and the table surface is$0.25$, then the maximum fraction of the length of the chain that can hang over one edge of the table is

1. $20\%$

2. $25\%$

3. $35\%$

4. $15\%$

Q. Some springs are combined in series and parallel arrangement as shown in the figure and a mass $m$ is suspended from them. The ratio of their frequencies will be

1. $\sqrt{3}:2$
2. $4:1$
3. $1:1$
4. $2:1$

Q.

A particle of mass 0.3 kg is subjected to a force F = -k x with k = 15 N/m. What will be its initial acceleration if it is released from a point x = 20 cm ?

Q. A mass of $0.2\text{kg}$ is attached to the lower end of a massless spring of force constant $200{\text{Nm}}^{-1}$, the upper end of which is fixed to a rigid support. Which of the following statement is true?

1. If the body is raised till the spring attains its natural length and then released, it will go down by $2\text{cm}$ before moving upwards
2. The frequency of oscillation will be nearly $50\text{Hz}$
3. In equilibrium, the spring will be stretched by $1\text{cm}$
4. All of the above

Q.

Consider two identical springs each of spring constant $k$ and negligible mass compared to the mass $M$ as shown. Fig.$1$ shows one of them and Fig. $2$ shows their series combination. The ratio of the time period of oscillation of the two S.H.M is $\frac{T_b}{T_a}=\sqrt{x}$, where the value of $x$ is ______. (Round off to the nearest integer)

Q. A mass $m$ is suspended from a spring of spring constant $K$ and just touches another identical spring fixed to the floor as shown in the figure. The time period of small oscillations is

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

Q. A block of 4kg is resting on a rough horizontal plane and is about to move. When a horizontal force of 30n is applied on it find the total contact force exerted by the plane on the block

Q. A carpet of mass $M$ made of inextensible material is rolled along its length in the form of a cylinder of radius $R$ and kept along a rough floor. The carpet starts unrolling without sliding on the floor when a negligibly small push is given to it. The horizontal velocity of the axis of the cylindrical part of the carpet, when its radius is reduced to $\frac{R}{2}$ is:

1. $\sqrt{\frac{14}{3}gR}$
2. $\sqrt{\frac{7}{3}gR}$
3. $\sqrt{gR}$
4. $\sqrt{2gR}$

Q.

When a mass m is hung from the lower end of a spring of negligible mass, an extension x is produced in the spring in equilibrium. The mass is set into vertical oscillations. The time period of oscillation is

1. $T=2\pi \sqrt{\frac{x}{mg}}$

2. $T=2\pi \sqrt{\frac{gx}{m}}$

3. $T=2\pi \sqrt{\frac{x}{g}}$

4. $T=2\pi \sqrt{\frac{x}{2g}}$

Q. A particle starts oscillating simple harmonically from its equilibrium position. Then the ratio of kinetic and potential energy of the particle at time $\frac{T}{12}$ is
($T=$ time period and assume potential energy at equilibrium position$=0$)

1. $2:1$
2. $3:1$
3. $4:1$
4. $1:4$

Q. A $10\text{kg}$ metal block is attached to a spring of spring constant $1000{\text{Nm}}^{-1}$. A block is displaced from equilibrium position by $10\text{cm}$ and released. The maximum acceleration of the block is

1. $10{\text{ms}}^{-2}$
2. $100{\text{ms}}^{-2}$
3. $200{\text{ms}}^{-2}$
4. $0.1{\text{ms}}^{-2}$

Q. A simple harmonic oscillator having four identical springs as shown in figure has time period (neglect the separation between the ends on the roof and the ends connected to the mass):

1. $2\pi \sqrt{\frac{m}{4k}}$
2. $2\pi \sqrt{\frac{m}{2k}}$
3. $2\pi \sqrt{\frac{m}{k}}$
4. $2\pi \sqrt{\frac{m}{8k}}$

Q.

A book of mass 5 kg is placed on a table and it is pressed by 10 N force then, normal force exerted by the table on the book is?

Q.

A spring stores 5 J of energy when stretched by 25 cm. It is kept vertical with the lower end fixed. A block fastened to its other end is made to undergo small oscillations. If the block makes 5 oscillations each second, what is the mass of the block ?

Q. $T_0$ is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to $\frac{1}{16}$ times of its initial value, the modified time period is :

1. $T_0$
2. $4T_0$
3. $\frac{1}{4}{T}_0$
4. $8\pi T_0$

Q.

The block of mass $m_1$ shown in figure (12-E2) is fastened to the spring and the block of mass $m_2$ is placed against it. (a) Find the compression of the spring in the equilibrium position. (b) The blocks are pushed a further distance $\left(2/k\right)(m_1+m_2)gsin\theta$ 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 ?

Q. A particle of mass $m$ is attached with four identical springs, each of length $l.$ Initially, each spring has tension $F_0$. Neglecting gravity, calculate the time period for small oscillations of the particle along a line perpendicular to the plane of the figure.

1. $T=2\pi \sqrt{\frac{ml}{F_0}}$
2. $T=2\pi \sqrt{\frac{ml}{2F_0}}$
3. $T=2\pi \sqrt{\frac{ml}{4F_0}}$
4. $T=2\pi \sqrt{\frac{4ml}{F_0}}$

Q. Find the time period of small oscillations for the block of mass $m$ as shown in the figure. [All springs are identical]

1. $T=2\pi \sqrt{\frac{3m}{2K}}$
2. $T=2\pi \sqrt{\frac{2m}{3K}}$
3. $T=2\pi \sqrt{\frac{m}{3K}}$
4. $T=2\pi \sqrt{\frac{m}{K}}$

Q. A coin placed on a rotating turntable just slip if it is placed at a distance of 4 cm from the center. If the angular velocity of the turntable is doubled, it will just slip at a distance of:

1. 5 cm
2. 6.5 cm
3. 1 cm
4. 3 cm

Q.

The restoring force in simple harmonic motion is _________ in magnitude when the particle is instantaneously at rest.

Q. A body at the end of a spring executes S.H.M. with a period $t_1,$ while the corresponding period for another spring is $t_2.$ If the period of oscillation with the two springs in series is $T$, then

1. $\frac{1}{T}=\frac{1}{t_1}+\frac{1}{t_2}$
2. $\frac{1}{T^2}=\frac{1}{t_1^2}+\frac{1}{t_2^2}$
3. $T=t_1+t_2$
4. $T^2=t_1^2+t_2^2$

Q. A particle is executing S.H.M. After 2 seconds of crossing the equilibrium position it is at a distance of $\frac{\sqrt{3}}{2}$ of its amplitude. Find its time period?

1. 3 s
2. 4 s
3. 12 s
4. 2 s

Q. A uniform rod of length $L$ and mass $M$ is pivoted at the centre. Its two ends are attached to two springs of equal spring constants $k$. The springs are fixed to rigid supports as shown in the figure and the rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle $\theta$ in one direction and released. The frequency of oscillation is

1. $\frac{1}{2\pi }\sqrt{\frac{24k}{M}}$
2. $\frac{1}{2\pi }\sqrt{\frac{2k}{M}}$
3. $\frac{1}{2\pi }\sqrt{\frac{6k}{M}}$
4. $\frac{1}{2\pi }\sqrt{\frac{k}{M}}$