Two identical springs have the same force constant 73.5 Nm^-1. The elongation produced in each spring in three cases shown in Figure-1, Figure- 2 and Figure- 3 are: (g = 9.8 ms^-2)

(1) $\frac{1}{6}m,\frac{2}{3}m,\frac{1}{3}m$

(2) $\frac{1}{3}m,\frac{1}{3}m,\frac{1}{3}m$

(3) $\frac{2}{3}m,\frac{1}{3}m,\frac{1}{6}m$

(4) $\frac{1}{3}m,\frac{4}{3}m,\frac{2}{3}m$

A particle of mass 10 g is undergoing SHM of amplitude 10 cm and period 0.1 sec. The maximum value of the force on the particle is about:

(1) 5.6 N

(2) 2.75 N

(3) 3.5 N

(4) 4 N

Which of the following graphs best represents the variation of acceleration 'a' of a particle executing SHM with displacement x?

(1) 

(2) 

(3) 

(4) 

Two masses m₁=1 kg and m₂=0.5 kg are executing SHM together suspended by a massless spring of spring constant 12.5 Nm^-1. When masses are in equilibrium, m₁ is removed without disturbing the system. The new amplitude of oscillation will be:

(1) 30 cm

(2) 50 cm

(3) 80 cm

(4) 60 cm

A mass m is attached to two springs of the same force constant K as shown in the following four arrangements. If $T_1, T_2, T_3$ and $T_4$ respectively be the time periods of oscillations in the following arrangements, in which case time period is maximum?

(1) 

(2) 

(3) 

(4) 

A particle of mass 4 kg moves simple harmonically such that its PE (U) varies with position x as shown in the figure. The period of oscillations is:

(1) $\frac{2\pi }{25} \mathrm{s}$

(2) $\frac{\pi \sqrt{2}}{5} \mathrm{s}$

(3) $\frac{4\pi }{5}$

(4) $\frac{2\pi \sqrt{2}}{5}s$ 

The kinetic energy and potential energy of a particle executing S.H.M. are equal when displacement in terms of amplitude 'A' is:

(1) $\frac{A}{2}$

(2) $\frac{A}{\sqrt{2}}$

(3) $\frac{A\sqrt{2}}{3}$

(4) $A\sqrt{2}$

Two identical pendulums oscillate with a constant phase difference $\frac{\mathrm{\pi }}{4}$ and the same amplitude. If the maximum velocity of one is v, the maximum velocity of the other will be:

(1) v

(2) $\sqrt{2}v$

(3) 2v

(4) $\frac{v}{\sqrt{2}}$

A simple pendulum suspended from the ceiling of a stationary lift has period T₀. When the lift descends at a steady speed, the period is T₁, and when it descends with constant downward acceleration, the period is T₂. Which one of the following is true?

(1) T₀ = T₁ = T₂

(2) T₀ = T₁ < T₂

(3) T₀ = T₁ > T₂

(4) T₀ < T₁ < T₂

If a Second's pendulum is moved to a planet where the acceleration due to gravity is 4 times the acceleration due to gravity on earth, to keep the time period of the second's pendulum same, the length of the second's pendulum on the planet should be made:

(1) 2 times

(2) 4 times

(3) 8 times

(4) 15 times