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

• mg (1 - θ₀)

• mg (1 + θ₀ )

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

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

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

A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes simple harmonic oscillations with a time period T. If the mass is increased by m, then the time period becomes $\left(\frac{5}{4} \mathrm{T}\right)$. The ratio of $\frac{\mathrm{m}}{\mathrm{M}}$ is

• 9/16

• 5/4

• 25/16

• 4/5

A wave is represented by the equation y= 0.5 sin(10t $-$ x) metre It is a travelling wave propagating along +x direction with velocity

• 10 m s^-1

• 20 m s^-1

• 5 m s^-1

• None of these