11.

A stone of relative density K is released from rest on the surface ofa lake. If viscous effects are ignored, the stone sinks in water with an acceleration of

• g (1 − K)

• g (1 + K)

• $\mathrm{g} \left(1 - \frac{1}{\mathrm{K}}\right)$

• $\mathrm{g} \left(1 + \frac{1}{\mathrm{K}}\right)$

A material has Poisson's ratio 0.50. If a uniform rod of it suffers a longitudinal strain of 2 x 10^-3 , then the percentage change in volume is

• 0.6

• 0.4

• 0.2

• zero

Two identical springs are connected to mass m as shown (k = spring constant). If the period of the configuration in (a) is 2s, the period of the configuration in (b) is

• $\sqrt{2} \mathrm{s}$

• 1 s

• $\frac{1}{\sqrt{2}} \mathrm{s}$ 

• $2\sqrt{2} \mathrm{s}$

An object weights m₁ in a liquid of density d₁ and that in liquid of density d₂ is m₂. The density d of the object is

• $\frac{{\mathrm{m}}_2{\mathrm{d}}_2 - {\mathrm{m}}_1{\mathrm{d}}_1}{{\mathrm{m}}_2 - {\mathrm{m}}_1}$

• $\frac{{\mathrm{m}}_1{\mathrm{d}}_1 - {\mathrm{m}}_2{\mathrm{d}}_2}{{\mathrm{m}}_{2 }- {\mathrm{m}}_1}$

• $\frac{{\mathrm{m}}_2{\mathrm{d}}_1 - {\mathrm{m}}_1{\mathrm{d}}_2}{{\mathrm{m}}_1 - {\mathrm{m}}_2}$

• $\frac{{\mathrm{m}}_1{\mathrm{d}}_2 - {\mathrm{m}}_2{\mathrm{d}}_1}{{\mathrm{m}}_1 - {\mathrm{m}}_2}$

A body floats in water with 40% of its volume outside water. When the same body floats in an oil. 60% of its volume remains outside oil. The relative density of oil is

• 0.9

• 1.0

• 1.2

• 1.5

Two soap bubbles of radii x and y coalesce to constitute a bubble of radius z. Then z is equal to 

• $\sqrt{{\mathrm{x}}^2 + {\mathrm{y}}^2}$

• $\sqrt{\mathrm{x} + \mathrm{y}}$

• x + y

• $\frac{\mathrm{x} + \mathrm{y}}{2}$

A particle of mass m is located in a one dimensional potential field where potential energy is given by V(x) = A(l − cos px), where A and p are constants. The period of small oscillations of the particle is 

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{\left(\mathrm{Ap}\right)}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{\left({\mathrm{Ap}}^2\right)}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{m}}{\mathrm{A}}}$

• $\frac{1}{2\mathrm{\pi }} \sqrt{\frac{\mathrm{Ap}}{\mathrm{m}}}$

The period of oscillation of a simple pendulum of length l suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination α is given by

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\mathrm{g} \cos \mathrm{\alpha }}}$

• $2\mathrm{\pi } \sqrt{\frac{\mathrm{l}}{\mathrm{g} \sin \mathrm{\alpha }}}$

• $2\mathrm{\pi }\sqrt{\frac{\mathrm{l}}{\mathrm{g}}}$

• $2\mathrm{\pi } \sqrt{\frac{\mathrm{l}}{\mathrm{g} \tan \mathrm{\alpha }}}$

A plane progressive wave is given by y = 2 cos 6.284 (330t − x). What is the period of the wave ? 

• $\frac{1}{330} \mathrm{s}$

• $2 \mathrm{\pi } \times 330 \mathrm{s}$

• ${\left(2\mathrm{\pi } \times 330\right)}^{-1} \mathrm{s}$

• $\frac{6.284}{330} \mathrm{s}$

The displacement of a particle is SHM varies according to the relation x = 4 (cos πt + sin πt). The amplitude of the particle is 

• − 4

• 4

• $4\sqrt{2}$

• 8