A liquid is kept in a cylindrical vessel which is being rotated about a vertical axis through the centre of the circular base. If the radius of the vessel is r and angular velocity of rotation is w, then the difference in the heights of the liquid at the centre of the vessel and the edge is

• $\frac{\mathrm{r} \mathrm{\omega }}{2 \mathrm{g}}$

• $\frac{{\mathrm{r}}^2 {\mathrm{\omega }}^2}{2 \mathrm{g}}$

• $\sqrt{2 \mathrm{gr} \mathrm{\omega }}$

• $\frac{{\mathrm{\omega }}^2}{2 {\mathrm{gr}}^2}$

A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of water in the capillary tube is 5 g. Another capillary tube of radius 2 r is immersed in water. The mass of water that will rise in this tube is

• 2.5 g

• 5.0 g

• 10 g

• 20 g

Neglecting  the  density  of  air, the  thermal  velocity  obtained  by  a  raindrop  of  radius  0.3  nm  falling  through  air  of  viscosity  1.8 × 10⁵ N s m²  will  be

• 10.9 m s^-1

• 7.48  m s^-1

• 3.7 m s^-1

• 12.8 m s^-1

Assertion:  Liquid molecules have greater potential energy at the melting point.

Reason:  Intermolecular spacing between molecules increases at melting point.

• If both assertion and reason are true and reason is the correct explanation of assertion.

• If both assertion and reason are true but reason is not the correct explanation of assertion.

• If assertion is true but reason is false.

• If both assertion and reason are false.

55.

Assertion: A needle placed carefully on the surface of water may float, whereas a ball of the same material will always sink.

Result: The buoyancy of an object depends both on the material and shape of the object.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false

In old age arteries carrying blood in the human body become narrow resulting in an increase in the blood pressure. This follows from

• Pascal's law

• Stoke's law

• Bernoulli's principle

• Archimede's principle

Which of the following physical quantities do not have same dimensions?

• pressure and stress

• tension and surface tension

• strain and angle

• energy and work

Work of 3.0 × 10^-4 joule is required to be done in increasing the size of a soap film from 10 cm ×  6 cm to 10 cm ×  11 cm. The surface tension of the film is

• 5 ×  10^-2 N/m

• 3 ×  10^-2 N/m

• 1.5 ×  10^-2 N/m

• 1.2 ×  10^-2 N/m

If the water falls from a dam into a turbine wheel 19.6 n below, then the velocity of water ar turbines  is ( Take g = 9.8 m/s )

• 9.8 m/s

• 19.6 m/s

• 39.2 m/s

• 98.6 m/s

Assertion: Machine parts are jammed in winter. 

Reason:  The viscosity of lubricant used in machine parts increase at low temperatures.

• If both assertion and reason are true and reason is the correct explanation of assertion

• If both assertion and reason are true but reason is not the correct explanation of assertion

• If assertion is true but reason is false

• If both assertion and reason are false