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)
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
The acceleration due to gravity becomes (g = acceleration due to gravity on the surface of the earth) at a height equal to
4R
2R
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
B.
144 J
At constant pressure,
Heat required = nCpΔT
⇒ 310 = 2 × Cp × (35 − 25)
⇒
Similarly, at constant volume,
Heat required = nCVΔT
= 2 (Cp − R) × (35 − 25) [Cp − CV = R]
= 2 × (15.5 − 8.30) × 10
= 2 × 7.2 × 10
= 144 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