Simple Pendulum

Q.

The bob of a simple pendulum has imparted a velocity of 5m/s when it is at its mean position. To what maximum vertical height will it rise on reaching at its extreme position if 60% of its energy is lost in overcoming the friction of air?(Take g=$10m{s}^{-2}$ ).

Q. A simple pendulum performs simple harmonic motion about x = 0 with an amplitude (A) and time period (T). The speed of the pendulum at $x=\frac{A}{2}$ will be

1. 
2. 
3. 
4. 

Q.

The energy changes in an oscillating pendulum is

1. Elastic potential energy and kinetic energy continuously interconvert such that Potential energy and kinetic energy are maximum at extreme positions and mean position respectively.

2. Gravitational potential energy and kinetic energy continuously interconvert such that Potential energy and kinetic energy are maximum at extreme positions and mean position respectively.

3. Gravitational potential energy and kinetic energy continuously interconvert such that Potential energy and kinetic energy are maximum at mean position and extreme positions respectively.

4. Elastic potential energy and kinetic energy continuously interconvert such that Potential energy and kinetic energy are maximum at mean position and extreme positions respectively.

Q. A pendulum clock having copper rod keeps correct time at ${20}^{\circ }$C. It gains 15 seconds per day if cooled to $0^{\circ }$C. Calculate the coefficient of linear expansion of copper.

1. $2.7\times {10}^{-5}{}^{\circ }{C}^{-1}$
2. $3.7\times {10}^{-5}{}^{\circ }{C}^{-1}$
3. $4.7\times {10}^{-5}{}^{\circ }{C}^{-1}$
4. $1.7\times {10}^{-5}{}^{\circ }{C}^{-1}$

Q.

A simple pendulum, while oscillating rises to a maximum vertical height of $5cm$ from its rest position. Assume its rest position is at ground level. If the mass of bob of the simple pendulum is $500g$ and acceleration due to gravity g = $10m/s^2$. Find the below:
i) The total energy of simple pendulum at any instant while oscillating.
ii) The velocity of bob at its resting position.

1. 0.25 J, 1 m/s

2. 0.25 J, 5 m/s

3. 0.30 J, 5 m/s

4. 0.30 J, 1 m/s

Q.

A pendulum is oscillating on either side of its rest position. Explain the energy changes that takes place in the oscillating pendulum. How does the mechanical energy remain constant in it? Draw the necessary diagram.

Q.

Name the type of energy possessed by the bob of a simple pendulum when it is at (a) the extreme position, (b) the mean position, and (c) between the mean and extreme positions.

Q.

A pendulum with bob of mass m is oscillating on either side from its resting position A between the extremes B and C at a vertical height h above A.What is the kinetic energy K and potential energy U when the pendulum is at positions (i) A, (ii) B, and (iii) C?

Q.

A diagram to show the energy changes in an oscillating simple pendulum is as follows:

The KE of the bob is the most when

1. The bob is at the mean position

2. The PE of the bob is the most

3. The bob is in-between the extreme position and the mean position

4. The bob is at the extreme position

Q.

If 2 pendulums of equal lengths are taken and suspended from an elastic string, they have same natural frequency and thus if one pendulum is displaced from mean position, the other also starts vibrating under resonance. But why there is a sharing of or transfer of energy between them and why their vibrations are in phase i.e., why when one amplitude is maximum, then the other pendulum has minimum amplitude?

Q. The bob of a simple pendulum is imparted a velocity of 5 metre per second when it is at its mean position. To what maximum vertical height will it rise on reaching at its extreme position if 60% of its energy is lost in overcoming the friction of air? (g = 10 m per second square)

Q. A body starts from rest and moving with an acceleration $5{\text{ms}}^{–2}$. The velocity of the body when it covers a distance of $100\text{m}$ (in ${\text{ms}}^{–1}$) is

1. $10\sqrt{2}{\text{ms}}^{–1}$
2. $10\sqrt{10}{\text{ms}}^{–1}$
3. $2\sqrt{10}{\text{ms}}^{–1}$
4. $10{\text{ms}}^{–1}$

Q.

The total energy of a swinging pendulum at any instant of time

1. remains zero

2. remains conserved

3. is same

4. is lost

Q.

For a simple pendulum bob, which of the following energies increase as it approaches the mean position?

1. Kinetic energy

2. Mechanical energy

3. Potential energy

4. Electrical energy

Q. A simple pendulum of length '$l$' has maximum angular displacement '$\theta$'. The maximum kinetic energy of the bob of mass 'm' is :
(g = acceleration due to gravity)

1. $mgl(1+cos\theta )$
2. $mgl(1+co{s}^2\theta )$
3. $mgl(1-cos\theta )$
4. $mgl(cos\theta -1)$

Q. A simple pendulum 1 metre long has a bob of 10 kg. lf the pendulum swings from a horizontal position, the kinetic energy of the bob, at the instant it passes through the lowest position of its path is: (Take $g=9.8/m/s^2$)

1. 89 joule
2. 95 joule
3. 98 joule
4. 85 joule

Q. A pendulum is oscillating on either side of its rest position. The correct statement is:

1. It has only the kinetic energy.
2. It has the maximum kinetic energy at its extreme position.
3. It has the maximum potential energy at its rest position.
4. The sum of its kinetic and potential energies remains constant throughout the motion.

Q. State the laws of simple pendulum.

Q.

A student is trying to measure the diameter of a lead shot using a screw gauge. The pitch of the screw gauge is 1 mm and has 50 divisions on its circular scale. When the two jaws of the screw gauge are in contact with each other, the zero of the circular scale lies 6 divisions below the line of graduation. When the lead shot is placed between the jaws, 3 linear scale divisions are clearly visible while ${31}^{st}$​ division on the circular scale coincides with the reference line. The diameter of the lead shot is:

1. 3.62 mm

2. 3.74 mm

3. 3.55 mm

4. 3.50 mm

Q. On a planet, a body released from rest is found to freely fall through a distance of 8 m in 2 s. On that planet what is the time period of a simple pendulum of length 1 m?

1. seconds.
2. seconds.
3. seconds.
4. seconds.

Q. The bob of a simple pendulum is displaced from its equilibrium position O to a position Q which is at height h above O and the bob is then released. Assuming the mass of the bob to be m and time period of osciliations to be 2.0 sec. the tension in the string when the bob passes through O is

1. $m(g+\pi \sqrt{2gh})$
2. $m(g+\sqrt{{\pi }^{2}gh})$
3. $m(g+\sqrt{\frac{{\pi }^2}{}gh})$
4. $m(g+\sqrt{\frac{{\pi }^2}{3}gh})$

Q.

The Bob of simple pendulum is imparted a velocity 5 m/s when it is at its mean position. To what maximum vertical height will it rise on reaching extreme position if 60% of its energy is lost in overcoming friction of air ? (g=10)

Q.

A simple pendulum, while oscillating rises to a maximum vertical height of $5cm$ from its rest position. Assume its rest position is at ground level. If the mass of bob of the simple pendulum is $500g$ and acceleration due to gravity g = $10m/s^2$. Find the below:
i) The total energy of simple pendulum at any instant while oscillating.
ii) The velocity of bob at its resting position.

1. 0.25 J, 1 m/s

2. 0.25 J, 5 m/s

3. 0.30 J, 5 m/s

4. 0.30 J, 1 m/s

Q. When a spring is compressed by 3 cm, the potential energy stored in it is U. When it is compressed further by 6 cm, the increase in potential energy is,

1. 4 U
2. U
3. 2 U
4. 3 U

Q. What energy changes take place in an oscillating pendulum?

Q. A pendulum is oscillating about its mean position in vacuum. It has:

1. Only kinetic energy
2. Maximum kinetic energy at extreme position
3. Sum of kinetic energy and potential energy remains constant throughout the motion
4. Maximum potential energy at its mean position

Q. A simple pendulum with bob of mass $m$ and length $x$ is held in position at an angle ${\theta }_1$, and then angle ${\theta }_2$ with the vertical. When released from these positions, speeds with which it passes the lowest positions are $v_1$ and $v_2$ respectively. Then $\frac{v_1}{v_2}$ is

1. $\frac{1-\cos {\theta }_1}{1-\cos {\theta }_2}$
2. $\sqrt{\frac{1-\cos {\theta }_1}{1-\cos {\theta }_2}}$
3. $\sqrt{\frac{2gx(1-\cos {\theta }_1)}{1-\cos {\theta }_2}}$
4. $\sqrt{\frac{1-\cos {\theta }_1}{2gx(1-\cos {\theta }_2)}}$

Q. During a swing in simple pendulum,

1. Potential energy remains constant
2. Total mechanical energy remains constant
3. All
4. Kinetic energy remains constant

Q. The bob of a pendulum is drawn aside so that it is at a height of $4.5m$ above the ground and released. If it reaches the equilibrium position which is at a height of $2m$ above the ground, the speed of the bob will be:

1. $7m/s$
2. $49m/s$
3. $7\sqrt{2}m/s$
4. $7/\sqrt{2}m/s$

Q. The bob of a pendulum is released from a horizontal position $A$ as shown in the figure. If the length of the pendulum is $1.5m$, what is the speed with which the bob arrives at the lower most point $B$, given that it dissipated $5$% of its initial energy against air resistance?

1. $5m/s$
2. $5.5m/s$
3. $5.3m/s$
4. $4.4m/s$