A mass of 10 g moving horizontally with a velocity of 100 cm/s strikes a pendulum bob of mass 10 g. The two masses stick together. The maximum height reached by the system now is (g = 10 m/s²)

• zero

• 5 cm

• 2.5 cm

• 1.25 cm

A particle of mass 10 g is executing simple harmonic motion with an amplitude of 0.5 m and periodic time of ($\mathrm{\pi }$/ 5) second. The maximum value of the force acting on the particle is

• 25 N

• 5 N

• 2.5 N

• 0.5 N

The period of vibration of a mass m suspended from a spring is 2 s. If along with it  another mass of 2 kg is also suspended, the period of oscillation increases by ls. The mass m will be

• 2 kg

• 1 kg

• 1.6 kg

• 2.6 kg

If length of a simple pendulum increases by 300%, then its time period increases by

• 100 %

• 200 %

• 300 %

• 400 %

Potential energy of a particle at a distance x from mean position, which is executing simple harmonic motion

• $\frac{1}{2} {\mathrm{m\omega }}^2{\mathrm{x}}^2$

• zero

• ${\mathrm{m}}^2\mathrm{\omega x}$

• $\frac{1}{2} {\mathrm{m}}^2{\mathrm{\omega }}^2{\mathrm{x}}^2$

A body executes simple harmonic motion under the action of force F₁ with a time period $\frac{4}{5}$s. If the force is changed to F₂ it executes simple harmonic motion with time period $\frac{3}{5} \mathrm{s}$.If both forces F₁ and F₂ act simultaneously in the same direction on the body, its time period will be

• $\frac{12}{25} \mathrm{s}$

• $\frac{24}{25} \mathrm{s}$

• $\frac{35}{24} \mathrm{s}$

• $\frac{15}{12} \mathrm{s}$

127.

A man measure time period of a pendulum (T) in stationary lift. If the lift moves upward with acceleration g /4, then new time period will be

• $\sqrt{\frac{2}{5}} \mathrm{T}$

• $\sqrt{\frac{5}{2}} \mathrm{T}$

• $\frac{\sqrt{5 }\mathrm{T}}{2}$

• $\frac{2 \mathrm{T}}{\sqrt{5}}$

A mass m is suspended from the two springs ofspring constants k₁ and k₂ as shown. The time period of vertical oscillations of the mass will be

• $2\mathrm{\pi }\sqrt{\left(\frac{{\mathrm{k}}_1 + {\mathrm{k}}_2}{\mathrm{m}}\right)}$

• $2\mathrm{\pi } \sqrt{\left(\frac{\mathrm{m}}{{\mathrm{k}}_1 + {\mathrm{k}}_2}\right)}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{m} \left({\mathrm{k}}_1 {\mathrm{k}}_2\right)}{{\mathrm{k}}_1 + {\mathrm{k}}_2}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{m} \left({\mathrm{k}}_1 + {\mathrm{k}}_2\right)}{\left({\mathrm{k}}_1 {\mathrm{k}}_2\right)}}$

A simple pendulum of length l has a maximum angular displacement Q. The maximum kinetic energy of the bob is

• mgl (1 - cosθ)

• 0.5 mgl

• mgl

• 2 mgl

A lift is ascending with an acceleration $\frac{\mathrm{g}}{3}$ . A simple pendulum suspended from its ceiling oscillates with a period T. The period of oscillation of pendulum when the lift is stationary will be

• $\frac{1}{\sqrt{3}} \mathrm{T}$

• T

• 2 T

• $\frac{2}{\sqrt{3}} \mathrm{T}$