JEE Main 2023 · 13 Apr 2023 Shift 1

A body of mass (5 ± 0.5) kg is moving with a velocity of (20 ± 0.4) m/s. Its kinetic energy will be

1. A(1000 ± 0.14) J
2. B(1000 ± 140) J
3. C(500 ± 0.14) J
4. D(500 ± 140) J

Two trains 'A' and 'B' of length 'l' and '4l' are travelling into a tunnel of length 'L' in parallel tracks from opposite directions with velocities 108 km/h and 72 km/h, respectively. If train 'A' takes 35s less time than train 'B' to cross the tunnel then, length 'L' of tunnel is : (Given L = 60 l)

1. A1800 m
2. B900 m
3. C1200 m
4. D2700 m

Two bodies are having kinetic energies in the ratio 16 : 9. If they have same linear momentum, the ratio of their masses respectively is :

1. A3 : 4
2. B9 : 16
3. C4 : 3
4. D16 : 9

A bullet of 10 g leaves the barrel of gun with a velocity of 600 m/s. If the barrel of gun is 50 cm long and mass of gun is 3 kg, then value of impulse supplied to the gun will be :

1. A12 Ns
2. B3 Ns
3. C6 Ns
4. D36 Ns

A planet having mass 9 Mₑ and radius 4 Rₑ, where Mₑ and Rₑ are mass and radius of earth respectively, has escape velocity in km/s given by: (Given escape velocity on earth Vₑ = 11.2 × 10³ m/s)

1. A67.2
2. B33.6
3. C16.8
4. D11.2

Under isothermal condition, the pressure of a gas is given by P = aV⁻³, where a is a constant and V is the volume of the gas. The bulk modulus at constant temperature is equal to

1. A3 P
2. B2 P
3. CP
4. DP/2

The rms speed of oxygen molecule in a vessel at particular temperature is (1 + 5/x)¹ᐟ² v, where v is the average speed of the molecule. The value of x will be : (Take π = 22/7)

1. A4
2. B8
3. C27
4. D28

The ratio of powers of two motors is ∛x/(√x + 1), that are capable of raising 300 kg water in 5 minutes and 50 kg water in 2 minutes respectively from a well of 100 m deep. The value of x will be

1. A2
2. B4
3. C16
4. D2·4