Simple Pendulum

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.

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, 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.

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.

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 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. 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. A point mass pendulum has initial velocity $v_0$ when passing through the vertical, and rises up so that the string makes some angle $\theta$ with the vertical, which corresponds to some maximum height $h$ for the pendulum.
If the initial speed were doubled to $2v_0$, what would the final height change to?

1. $h/4$
2. $4h$
3. $\sqrt{2}h$
4. $2h$
5. $h$

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