An ice-cube of density 900 kg /m³ is floating in water of density 1000 kg / m³. The percentage of volume of ice-cube outside the water is

• 20%

• 35%

• 10%

• 25%

A sphere of diameter 0.2 m and mass 2 kg is rolling on an inclined plane with velocity u = 0.5 mls. The kinetic energy of the sphere is

• 0.1 J

• 0.3 J

• 0.5 J

• 0.42 J

A particle is executing the motion x = αcos(ωt-θ).The velocity of the particle is

• αω cosθ

• αω

• αω sinθ

• None of the above

 A particle is executing two different simple harmonic motions, mutually perpendicular, of different amplitudes and having phase difference of $\frac{\mathrm{\pi }}{2}$ The path of the particle will be

• circular

• straight line

• parabolic

• elliptical

Equations of motion in the same direction are given by

$$\begin{gathered} {\mathrm{y}}_1 =2\mathrm{\alpha } \sin \left(\mathrm{\omega t} -\mathrm{kx}\right) \\ {\mathrm{y}}_2 =2\mathrm{\alpha } \sin \left(\mathrm{\omega t} -\mathrm{kx}-\mathrm{\theta }\right) \end{gathered}$$

The amplitude of the medium particle will be

• $2\mathrm{\alpha } \mathrm{cos\theta }$

• $\sqrt{2}\mathrm{\alpha } \mathrm{cos\theta }$

• $4\mathrm{\alpha } \cos \frac{\mathrm{\theta }}{2}$

• $\sqrt{2}\mathrm{\alpha } \cos \frac{\mathrm{\theta }}{2}$

A closed argon pipe and an open argon pipe are tuned to the same fundamental frequency. What is the ratio of their lengths?

• 1:2

• 2:1

• 2:3

• 4:3

A steel scale measures the length of a copper wire as 80.0 cm, when both are at 20C, the calibration temperature for the scale. What would the scale read for the length of the rod when both are at 40°C?

Given α for steel = 11 × 10^-6 per ^oC and 

α for Cu = 11×10^-6 per ^oC

• 80.0096 cm

• 80.0272 cm

• 1 cm

• 25.2 cm

A tank is filled with water upto height H. When a hole is made at a distance h below the level of water. What will be the horizontal range of water jet?

• $2 \sqrt{\mathrm{h} \left(\mathrm{H} - \mathrm{h}\right)}$

• $4 \sqrt{\mathrm{h} \left(\mathrm{H} + \mathrm{h}\right)}$

• $4 \sqrt{\mathrm{h} \left(\mathrm{H} - \mathrm{h} \right)}$

• $2 \sqrt{\mathrm{h} \left(\mathrm{H} + \mathrm{h}\right)}$

19.

A raft of wood of mass 120 kg floats in water. The weight that can be put on the raft to make it just sink, should be (d _raft = 600 kg/m³)

• 80 kg

• 50 kg

• 60 kg

• 30 kg

A monoatomic gas supplied the heat Q very slowly keeping the pressure constant. The work done by the gas will be

• $\frac{2}{3}\mathrm{Q}$

• $\frac{3}{5 }\mathrm{Q}$

• $\frac{2}{5}\mathrm{Q}$

• $\frac{1}{5}\mathrm{Q}$