A particle executes SHM of amplitude 4 cm and time period 2 s. Then, the time taken by it to move from positive extreme position to half the amplitude is

• $\frac{1}{3} \mathrm{s}$

• $\frac{1}{2} \mathrm{s}$

• $\frac{1}{4} \mathrm{s}$

• 2 s

An organ pipe open at one end is vibrating in second harmonic and is in resonance with another pipe open at both the ends and vibrating in second overtone. The ratio of length of two pipes is

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{3}{4}$

• $\frac{3}{2}$

A simple pendulum of length l₁ has a time period of 2 s and another pendulum of length l₂ has a time period of 1 s. Then, the time period of pendulum having length l₁ − l₂ will be

• 2 s

• 1.2 s

• 3 s

• $\sqrt{3}$ s

Springs of spring constants K, 2K,4K, 8K...are connected in series.A mass m kg is attached to the lower end of the last spring and the system is allowed to vibrate. The time period of oscillations is (Given, m= 40 g and k =2.0 N-cm^-1)

• 2.12 s

• 0.126 s

• 1.26 s

• 0.0126 s

A pendulum made of a uniform wire of cross-sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to T_m . If the Young's modulus of the material is Y, then $\frac{1}{\mathrm{Y}}$ is equal to

• $\left[{\left(\frac{{\mathrm{T}}_{\mathrm{m}}}{\mathrm{T}}\right)}^2 - 1\right]\frac{\mathrm{A}}{\mathrm{Mg}}$

• $\left[{\left(\frac{{\mathrm{T}}_{\mathrm{m}}}{\mathrm{T}}\right)}^2 - 1\right]\frac{\mathrm{Mg}}{\mathrm{A}}$

• $\left[1 - {\left(\frac{{\mathrm{T}}_{\mathrm{m}}}{\mathrm{T}}\right)}^2\right]\frac{\mathrm{A}}{\mathrm{Mg}}$

• $\left[1 - {\left(\frac{\mathrm{T}}{{\mathrm{T}}_{\mathrm{m}}}\right)}^2\right]\frac{\mathrm{A}}{\mathrm{Mg}}$

Which of the following graphs represents resonance for low damping ?

• graph (1)

• graph (2)

• graph (3)

• None of these

A magnet is made to oscillate with a particular frequency, passing through a coil as shown in the figure. The time variation of the magnitude of emf generated across the coil during one cycle is

A particle executes simple harmonic motion between x = − A and x = + A. The time taken for it to go from O to A/ 2 is T₁ and to go from A/2 to A is T₂ . Then

• T₁ < T₂

• T₁ > T₂

• T₁ = T₂

• T₁ = 2T₂

A body executes simple harmonic motion. The potential energy (PE), kinetic energy (KE) and total energy (TE) are measured as a function of displacement y. Which of the following statements is true ?

• TE is zero when x = 0

• PE is maximum when x = 0

• KE is maximum when x = O

• KE is maximum when x is maximum

140.

The KE and PE of a particle executing SHM of amplitude a will be equal when displacement is

• $\frac{\mathrm{a}}{2}$

• $\mathrm{a}\sqrt{2}$

• 2a

• $\frac{\mathrm{a}}{\sqrt{2}}$