A refrigerator is to maintain eatables kept inside at 9°C. If room temperature is 36° C, Calculate the coefficient of performance.

30.90

28.20

20.40

10.44

In an inelastic collision of two bodies, the quantities which do not change after the collision

total kinetic energy

total linear momentum

total energy of the system of two bodies

A trolley of mass 200 kg moves with a uniform speed of 36 km/h on a frictionless track.A child of mass 20 kg runs on the trolley from one end to the other (10 m away) with a speed of 4 \(\large m \,s^{–1}\) relative to the trolley in a direction opposite to the its motion, and jumps
out of the trolley. What is the final speed of the trolley?

\(\large 25.90 \, m\, s^{-1}\)

\(\large 22.80 \, m\, s^{-1}\)

\(\large 10.36 \, m\, s^{-1}\)

\(\large 5.18 \, m\, s^{-1}\)

A bullet of mass 0.012 kg and horizontal speed 70 \(\large ms^{-1}\) strikes a block of wood of mass 0.4 kg and instantly comes to rest with respect to the block. The block is suspended from the ceiling by means of thin wires. Calculate the height to which the block rises.

0.212 m

0.424 m

0.530 m

0.636 m

The escape speed of a projectile on the earth’s surface is 11.2 km \(\large s^{–1}\). A body is projected out with thrice this speed. What is the speed of the body far away from the earth? Ignore the presence of the sun and other planets.

15.85 Km/s

31.7 Km/s

39.7 Km/s

39.7 Km/s

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface?

125 N

200 N

225 N

250 N

A Saturn year is 29.5 times the earth year. How far is the Saturn from the sun if the earth is \(\large 1.50 ×10^{8}\) km away from the sun?

\(\large 1.43 \times 10^{15}\)

\(\large 1.43 \times 10^{13}\)

\(\large 1.43 \times 10^{12}\)

\(\large 1.43 \times 10^{11}\)

A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero?  Mass of the sun = \(\large 2 ×10^{30}\) kg, mass of the earth = \(6 × 10^{24}\) kg.

Neglect the effect of other planets etc. (orbital radius = \(1.5 × 10^{11}\) m).

\(\large 1.3 \times 10^{8} \,m\)

\(\large 2.6 \times 10^{8} \,m\)

\(\large 2.6 \times 10^{10} \,m\)

\(\large 2.6 \times 10^{11} \,m\)

An electric heater supplies heat to a system at a rate of 100W. If system performs work at a rate of 75 Joules per second. At what rate is the internal energy increasing?

60 J/s

50 J/s

25 J/s

20 J/s

A steam engine delivers \(\large 5.4×10^8\) J of work per minute and services \(\large 3.6 × 10^9\) J of heat per minute from its boiler. What is the efficiency of the engine?

15 %

20 %

25 %

30 %

Two cylinders A and B of equal capacity are connected to each other via a stopcock. A contains a gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stopcock is suddenly opened.What is the final pressure of the gas in A and B?

0 atm

0.5 atm

1 atm

1.5 atm

A cylinder with a movable piston contains 3 moles of hydrogen at standard temperature and pressure. The walls of the cylinder are made of a heat insulator, and the piston is insulated by having a pile of sand on it. By what factor does the pressure of the gas increase if the gas is compressed to half its original volume?

1.32 

1.98

2.64

3.96

What amount of heat must be supplied to \(\large 2.0 × 10^{–2}\) kg of nitrogen (at room temperature) to raise its temperature by 45 °C at constant pressure?
(Molecular mass of N2 = 28; R = \(\large 8.3 \,J \,mol^{–1} K^{–1}\).)

466.69 J

933.38 J.

1400.07 J

1866.76 J

A geyser heats water flowing at the rate of 3.0 litres per minute from 27 °C to 77 °C. If the geyser operates on a gas burner, what is the rate of consumption of the fuel if its heat of combustion is \(\large 4.0 × 10^4\) J/g?

15.75 g/min

31.50 g/min

45.75 g/min

63.00 g/min

A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time t is proportional to

\(\large t^{\frac{1}{2}}\)

\(\large t\)

\(\large t^{\frac{3}{2}}\)

\(\large t^{2}\)

Which of the following statements is TRUE

In an elastic collision of two bodies, the momentum and energy of each body is conserved.

Total energy of a system is always conserved, no matter what internal and external forces on the body are present.

Work done in the motion of a body over a closed loop is zero for every force in nature.

In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.

Comets move around the sun in highly elliptical orbits. The gravitational force on the comet due to the sun is not normal to the comet’s velocity in general. Yet the work done by the gravitational force over every complete orbit of the comet is

2

1

0

-1

A body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7 N on a table with coefficient of kinetic friction = 0.1. Compute the work done by the  applied force in 10 s, work done by friction in 10 s, work done by the net force on the body in 10 s.

882 J, 247 J, 635 J

882 J, –247 J, 635 J

630 J, –247 J, 635 J

882 J, –247 J, 1129 J

Which of the following symptoms is not likely to afflict an astronaut in space

swollen feet

swollen face

headache

orientational problem

Let us assume that our galaxy consists of \(\large 2.5 × 10^{11}\) stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be \(\large 10^5\) ly.

\(\large 0.06 \times 10^{16} s\)

\(\large 1.12 \times 10^{8} s\)

\(\large 1.12 \times 10^{12} s\)

\(\large 1.12 \times 10^{16} s\)

Suppose there existed a planet that went around the sun twice as fast as the earth.What would be its orbital size as compared to that of the earth?

Less by 0.63

Less by 0.31

More by 0.63

More by 0.32

A cycle tyre bursts suddenly. What is the type of this process?

Isothermal

Adiabatic

Isochoric

Isobaric

What is the source temperature of the Carnot engine required to get 70% efficiency? Given sink temperature = \(\large 27^{\circ}\)

\(\large 1000^{\circ} C\)

\(\large 90^{\circ} C\)

\(\large 270^{\circ} C\)

\(\large 727^{\circ} C\)

A hot body is allowed to cool. The surrounding temperature is constant at 30\(\large ^{0}\) C. The body takes time t\(\large _{1}\) to cool from 90\(\large ^{0}\) C to 89\(\large ^{0}\) C and time t2 to cool from 60\(\large ^{0}\) C to 59.5\(\large ^{0}\) C. Then,

\(\large t_{2}=\frac{t_{1}}{2}\)

\(\large t_{2}=2t_{1} \)

\(\large t_{2}=t_{1} \)

\(\large t_{2}=4t_{1} \)

Earth is moving around the Sun in elliptical orbit as shown. The ratio of OB and OA is R. Then the ratio of Earth at A and B is

R\(\large ^{-1}\)

\(\large \sqrt{R}\)

R

R\(\large ^{\frac{2}{3}}\)

Non of the above

From a fixed support, two small identical spheres are suspended by means of strings of length 1 m each. They are pulled aside as shown and then released. B is the mean position. Then the two spheres collide.

at B after 0.25 second

at B after 0.5 second

on the right side of B after some time

on the right side of B when the strings are inclined at 150 with B

A gun fires a small bullet with kinetic energy K. Then kinetic energy of the gun while recoiling is

K

more than K

less than K

\(\large \sqrt{k}\)

A planet moving around sun sweeps area A\(\large _{1}\) in 2 days, A\(\large _{2}\) in 3 days and A\(\large _{3}\) in 6 days. Then the relation between A\(\large _{1}\), A\(\large _{2}\) and A\(\large _{3}\) is

6 A\(\large _{1}\) = 3 A\(\large _{2}\) = 2 A\(\large _{3}\)

3 A\(\large _{1}\) = 2 A\(\large _{2}\) = 6 A\(\large _{3}\)

2 A\(\large _{1}\) = 3 A\(\large _{2}\) = 6 A\(\large _{3}\)

3 A\(\large _{1}\) = 2 A\(\large _{2}\) = A\(\large _{3}\)

The following four wires of length L and radius r are made of the same material. Which of these will have the largest extension, when the same tension is applied?

L = 200 cm, r = 0.4 mm

L = 300 cm, r = 0.6 mm

L = 400 cm, r = 0.8 mm

L = 100 cm, r = 0.2 mm

Two satellites of mass m and 9 m are orbiting a planet in orbits of radius R. Their periods of revolution will be in the ratio of ……..

3: 1

1: 1

1: 3

9: 1