A particle is executing simple harmonic motion with amplitude A. When the ratio of its kinetic energy to the potential energy is $\frac{1}{4}$, its displacement from its mean position is

• $\frac{2}{\sqrt{5}} \mathrm{A}$

• $\frac{\sqrt{3}}{2} \mathrm{A}$

• $\frac{3}{4} \mathrm{A}$

• $\frac{1}{4} \mathrm{A}$

The ratio of amplitudes of two simple harmonic motions represented by the equations ${\mathrm{y}}_1 = 5 \sin \left(2\mathrm{\pi t} + \frac{\mathrm{\pi }}{4}\right)$ and ${\mathrm{y}}_2 = 2\sqrt{2} \left(\sin 2\mathrm{\pi t} + \cos 2\mathrm{\pi t}\right)$ is

• 1 : 1

• 2 : 1

• 5 : 2

• 5 : 4

The displacement of a particle in SHM is $\mathrm{x} = 10 \sin \left(2\mathrm{t} - \frac{\mathrm{\pi }}{6}\right)$ m. When its displacement is 6 m, the velocity of the particle (in ms^-1) is

• 8

• 24

• 16

• 10

The bulk modulus of a liquid of density 8000 kgm^-3 is 2 x 10⁹ Nm^-2. The speed of sound in that liquid is (in ms^-1)

• 200

• 250

• 500

• 350

35.

The vibrations of a string of length 60 cm fixed at both the ends are represented by the equation $\mathrm{y} = 2 \sin \left(\frac{4\mathrm{\pi x}}{15}\right) \cos \left(96\mathrm{\pi t}\right)$, where x and y are in cm. The maximum number of loops that can be formed in it, is

• 6

• 16

• 5

• 15

The pressure variations in the propagation of sound waves are

• isobaric

• isochoric

• isobaric and isochoric

• adiabatic

A steel plate of size 6 cm x 6 cm is to be coated by a metal on both sides with a coating thickness of 0.1 mm by electrolysis. If the density and ece of the metal are respectively 10 g cm^-3 and 0.001 gC^-1 then the strength of the current to complete the process in one hour is

• 1 A

• 0.5 A

• 6 A

• 2 A

A signal of 5 kHz frequency modulates a carrier of frequency 1 MHz and peak voltage 25 V. If the amplitude at the sidebands of the amplitude modulated signal is 5 V, then the modulation index is

• 0.8

• 0.6

• 0.4

• 0.2

An uncharged parallel plate capacitor filled with a dielectric of dielectric constant K is connected to an air filled identical parallel capacitor charged to potential V₁. If the common potential is V₂, the value of K is

• $\frac{{\mathrm{V}}_1 - {\mathrm{V}}_2}{{\mathrm{V}}_1}$

• $\frac{{\mathrm{V}}_1}{{\mathrm{V}}_1 - {\mathrm{V}}_2}$

• $\frac{{\mathrm{V}}_2}{{\mathrm{V}}_1 - {\mathrm{V}}_2}$

• $\frac{{\mathrm{V}}_1 - {\mathrm{V}}_2}{{\mathrm{V}}_2}$

When a comb rubbed with dry hair attracts pieces of paper. This is because the

• comb polarizes the piece of paper

• comb induces a net dipole moment opposite to the direction of field

• electric field due to the comb is uniform

• comb induces a net dipole moment perpendicular to the direction of field