A lens with refractive index \( \frac{3}{2} \) has a power of +5 diopters in air. If it is completely immersed in water, its power is (in diopters).The refractive index of water is \( \frac{4}{3} \)
A metal rod of 50 cm length is clamped at its midpoint and is set to vibrations. The density of that metal is \( 2 \times 10^3 \, {kg/m}^3 \).Young's modulus of that metal is \( 8 \times 10^8 \, {Nm}^2 \). The fundamental frequency of the vibration is
The oxygen gas of 5 moles is heated at constant pressure from 300 K to 320 K. The amount of energy spent during this expansion is (For oxygen \( C_p = 7 \, {Cal/mol} \cdot \degree C \), \( C_v = 5 \, {Cal/mol} \cdot \degree C \))
The mass 'm' oscillates in simple harmonic motion with an amplitude 'A' as shown in the figure. The amplitude of point \(P\) is
The relation between velocity \( V \) (in ms\(^{-1}\)) and the displacement \( x \) (in meters) of a particle in motion is \( 2V = \sqrt{37 + 32x} \). The acceleration of the particle is