The net force acting is not zero on

• a retarding train

• a ball falling with terminal velocity

• a kite held stationary

• a truck moving with constant velocity

An engine of power 58.8 kW pulls a train of mass 2x10⁵ kg with a velocity of 36 kmh^-1. The coefficient of friction is

• 0.3

• 0.03

• 0.003

• 0.0003

If a capillary tube of radius r is immersed in a liquid, then the liquid rises to a height h. The corresponding mass of liquid column is m. The mass of water that would rise in another capillary tube of twice the radius is

• 2 m

• 5 m

• 3 m

• 4 m

In a horizontal pipe of non-uniform cross-section, water flows with a velocity of 1 ms^-1 at a point where the diameter of the pipe is 20 cm. The velocity of water (in ms^-1) at a point where the diameter of the pipe is 5 cm is

• 64

• 24

• 16

• 32

A spherical ball of diameter 1 cm and density 5 x 10³ kg m^-3 is dropped gently in a large tank containing viscous liquid of density 3 x10³ kg m^-3 and coefficient of viscosity 0.1 Ns m^-2. The distance, the ball moves in 1 s after attaining terminal velocity is (g =10 ms^-2)

• $\frac{10}{9} \mathrm{m}$

• $\frac{2}{3} \mathrm{m}$

• $\frac{4}{9} \mathrm{m}$

• $\frac{4}{5} \mathrm{m}$

The Zeroth law of thermodynamics leads to the concept of

• internal energy

• heat content

• pressure

• temperature

The difference between the specific heats of a gas is 4150 Jkg^-1 K^-1. If the ratio of specific heat is 1.4, then the specific heat at constant volume of the gas (in J kg^-1 K^-1) is

• 1037.5

• 2037.5

• 8300

• 10375

The Carnot cycle of a reversible heat engine consists of

• one isothermal and two adiabatic processes

• two isothermal and one adiabatic processes

• two isothermal and two adiabatic processes

• two isobaric and two isothermal processes

Two equal masses hung from two massless springs of spring constants k₁ and k₂. They have equal maximum velocity when executing simple harmonic motion. The ratio of their amplitudes is

• ${\left(\frac{{\mathrm{k}}_1}{{\mathrm{k}}_2}\right)}^{1/2}$

• $\left(\frac{{\mathrm{k}}_1}{{\mathrm{k}}_2}\right)$

• $\left(\frac{{\mathrm{k}}_2}{{\mathrm{k}}_1}\right)$

• ${\left(\frac{{\mathrm{k}}_2}{{\mathrm{k}}_1}\right)}^{1/2}$

30.

The simple harmonic motion of a particle is given by x = a sin 2$\mathrm{\pi }$t. Then, the location of the particle from its mean position at a time 1/8th of a second is

• a

• $\frac{\mathrm{a}}{2}$

• $\frac{\mathrm{a}}{\sqrt{2}}$

• $\frac{\mathrm{a}}{4}$