A mass of 1 kg is suspended from a spring of force constant 400 N, executing SHM total energy of the body is 2J, then maximum acceleration of the spring will be

• 4 m/s²

• 40 m/s²

• 200 m/s²

• 400 m/s²

Vibrations of rope tied by two rigid ends shown by equation y = cos 2πt sin2πx, then minimum length of the rope will be

• 1 m

• $\frac{1}{2}\mathrm{m}$

• 5 m

• 2πm

The angular amplitude of a simple pendulum is θ₀. The maximum tension in its string will be

• mg (1 - θ₀)

• mg (1 + θ₀ )

• $\mathrm{mg} \left(1- {\mathrm{\theta }}_0^2\right)$

• $\mathrm{mg} \left(1 + {\mathrm{\theta }}_0^2\right)$

64.

A particle is subjected to two simple harmonic motions along X-axis while other is along a line making angle 45° with the X-axis. The two motions are given by   x = x₀ sin ωt  and  s =s₀ sin ωt. The amplitude of resultant motion is 

• x₀ + s₀ + 2x₀s₀

• $\sqrt{{\mathrm{x}}_0^2 + {\mathrm{s}}_0^2}$

• $\sqrt{{\mathrm{x}}_0^2 - {\mathrm{s}}_0^2 + 2{\mathrm{x}}_0 {\mathrm{s}}_0}$

• ${\left[{\mathrm{x}}_0^2 + {\mathrm{s}}_0^2 + \sqrt{2} {\mathrm{x}}_0 {\mathrm{s}}_0\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

A pan with a set of weights is attached to a light spring. The period of vertical oscillation is 0.5s. When some additional weights are put in pan, then the period of oscillations increases by 0.1 s. The extension caused by the additional weight is

• 5.5 cm

• 3.8 cm

• 2.7 cm

• 1.3 cm

A particle is describing simple harmonic motion. If its velocities are v₁ and v₂ when the displacements from the mean position are y₁ and y₂ respectively, then its time period is

• $2\mathrm{\pi } \sqrt{\frac{{\mathrm{y}}_1^2 + {\mathrm{y}}_2^2}{{\mathrm{v}}_1^2 + {\mathrm{v}}_2^2}}$

• $2\mathrm{\pi } \sqrt{\frac{{\mathrm{v}}_2^2 - {\mathrm{v}}_1^2}{{\mathrm{y}}_1^2 - {\mathrm{y}}_2^2}}$

• $2\mathrm{\pi } \sqrt{\frac{{\mathrm{v}}_1^2 + {\mathrm{v}}_2^2}{{\mathrm{y}}_1^2 + {\mathrm{y}}_2^2}}$

• $2\mathrm{\pi } \sqrt{\frac{{\mathrm{y}}_1^2 - {\mathrm{y}}_2^2}{{\mathrm{v}}_2^2 - {\mathrm{v}}_1^2}}$

Assertion:  A particle in x-y plane is related by   x = $\mathrm{\alpha }$ sin t and  y =  $\mathrm{\alpha }$ (l - cos t), where $\mathrm{\alpha }$ and ω are constants, then the particle will have parabolic motion.

Reason:  A particle under the influence of two perpendicular velocities has parabolic motion.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

A body of mass 60 kg is suspended by means of three strings P Q and R as shown in the figure is in equilibrium. The tension in the string P is

• 130.9 g N

• 60 g N

• 50 g N

• 103.9 g N

The angular amplitude of simple pendulum is θ_o. The maximum tension in its string will be

• mg ( 1 - θ₀ )

• mg ( 1 + cosθ₀)

• mg ( 1 - cos)

• mg ( 1 + cos)

The displacement of a particle executing SHM is given by y = 0.25 sin200t cm. The maximum speed of the particle is

• 200 cm s^-1

• 100 cm s^-1

• 50 cm s^-1

• 5.25 cm s^-1