The dimensional formula for impulse is

• [MLT^-1]

• [ML^-1T]

• [M^-1LT^-1]

• [ML^-1T^-1]

The maximum height attained by a projectile when thrown at an angle θ with the horizontal is found to be half the horizontal range. Then θ is equal to

• tan^-1 (2)

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{4}$

• ${\tan }^{-1} \left(\frac{1}{2}\right)$

A shell of mass 20 kg at rest explodes into two fragments whose masses are in the ratio 2 : 3. The smaller fragment moves with a velocity of 6 ms^-1. The kinetic energy of the larger fragment is

• 96 J

• 216 J

• 144 J

• 360 J

4.

The acceleration due to gravity becomes $\left(\frac{\mathrm{g}}{2}\right)$ (g = acceleration due to gravity on the surface of the earth) at a height equal to

• 4R

• $\frac{\mathrm{R}}{4}$

• 2R

• $\frac{\mathrm{R}}{2}$

Water rises in plant fibres due to

• capillarity

• viscosity

• fluid pressure

• osmosis

The cylindrical tube of a spray pump has a cross-section of 8 cm², one end of which has 40 fine holes each of area 10^-8 m². Ifthe liquid flows inside the tube with a speed of 0.15 m min^-1 the speed with which the liquid is ejected through the holes is

• 50 ms^-1

• 5 ms^-1

• 0.05 ms^-1

• 0.5 ms^-1

During an adiabatic process, the cube of the pressure is found to be inversely proportional to the fourth power of the volume. Then the ratio of specific heats is

• 1

• 1.33

• 1.67

• 1.4

Two identical rods AC and CB made of two different metals having thermal conductivities in the ratio 2 : 3 are kept in contact with each other at the end C as shown in the figure. A is at 100°C and B is at 25°C. Then the junction C is at

• 55°C

• 60°C

• 75°C

• 50°C

310 J of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from 25°C to 35°C. The amount of heat required to raise the temperature of the gas through the same range at constant volume is

• 384 J

• 144 J

• 276 J

• 452 J

A Carnot's engine operates with source at 127°C and sink at 27°C. If the source supplies 40 kJ of heat energy, the work done by the engine is

• 30 kJ

• 10 kJ

• 4 kJ

• 1 kJ