A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A body suspended from this balance, when displaced and released, oscillates with a period of 0.6 s. What is the weight of the body?

1. 219 N

2. 196 N

3. 223 N

4. 225 N

A spring having a spring constant of \(1200\) N/m is mounted on a horizontal table as shown in the figure. A mass of \(3\) kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of \(2.0\) cm and released. The frequency of oscillations will be:
    

A spring having a spring constant of \(1200\) N/m is mounted on a horizontal table as shown in the figure. A mass of \(3\) kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of \(2.0\) cm and released. The maximum acceleration of the mass is:

The piston in the cylinder head of a locomotive has a stroke (twice the amplitude) of 1.0 m. If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what is its maximum speed?

1. 50 m/min
2. 150 m/min
3. 100 m/min
4. 120 m/min

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

1. 7.3 s
2. 6.4 s
3. 5.5 s
4. 8.4 s

What is the frequency of oscillation of a simple pendulum mounted in a cabin that is freely falling under gravity?

A simple pendulum of length l and having a bob of mass M is suspended in a car. The car is moving on a circular track of radius R with a uniform speed v. If the pendulum makes small oscillations in a radial direction about its equilibrium position, what will be its time period?
1. \(\mathrm{T}=2 \pi \sqrt{\frac{1}{\sqrt{\mathrm{g}^2+\frac{\mathrm{v}^4}{\mathrm{R}^2}}}}\)
2. \(\mathrm{T}=4 \pi \sqrt{\frac{\mathrm{l}}{\mathrm{g}^2+\frac{\mathrm{v}^4}{\mathrm{R}^2}}}\)
3. \(\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{l}}{\mathrm{g}^2+\frac{\mathrm{v}^3}{\mathrm{R}^2}}}\)
4. \(\mathrm{T}=4 \pi \sqrt{\frac{1}{\sqrt{\mathrm{g}^2+\frac{\mathrm{v}^4}{\mathrm{R}^4}}}}\)

A cylindrical piece of cork of density $\mathrm{\rho }$ and base area A and height h floats in a liquid of density ${\mathrm{\rho }}_{\mathrm{l}}$. The cork is depressed slightly and then released. If the cork oscillates up and down simple harmonically then its period is
1. \(\mathrm{T}=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{h} \rho}{\rho_1 \mathrm{~g}}}\)
2. \(\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{h} \rho}{\rho_{\mathrm{l}} \mathrm{g}}}\)
3. \(\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{h} \rho_1}{\rho \mathrm{g}}}\)
4. \(\mathrm{T}=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{h} \rho_1}{\rho \mathrm{g}}}\)

An air chamber of volume V has a neck area of cross-section 'a' into which a ball of mass 'm' just fits and can move up and down without any friction (as shown in the figure). When the ball is pressed down a little and released, it executes SHM. The time period of oscillations is:

(assuming pressure-volume variations of air to be isothermal)
   
1. \(\mathrm{T}=\frac{1}{2 \pi} \sqrt{\frac{\mathrm{Vm}_{\mathrm{m}}}{\mathrm{Ba}^3}}\)
2. \(\mathrm{T}=\pi \sqrt{\frac{\mathrm{Vm}_{\mathrm{m}}}{\mathrm{Ba}^2}}\)
3. \(\mathrm{T}=2 \pi \sqrt{\frac{\mathrm{Vm}_{\mathrm{m}}}{\mathrm{Ba}^2}}\)
4. \(\mathrm{T}=3 \pi \sqrt{\frac{\mathrm{Vm}_{\mathrm{m}}}{\mathrm{Ba}^2}}\)

A circular disc of mass 10 kg is suspended by a wire attached to its centre. The wire is twisted by rotating the disc and released. The period of torsional oscillations is found to be 1.5 sec. The radius of the disc is 15 cm. The torsional spring constant of the wire is:
1. 2.1 Nm rad⁻¹
2. 0.6 Nm rad⁻¹
3. 3.2 Nm rad⁻¹
4. 1.9 Nm rad⁻¹