A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 ms^–1. To give an initial upward acceleration of 20 ms^–2, the amount of gas ejected per second to supply the needed thrust will be (g = 10 ms^–2) 

(1) 127.5 kg s^–1

(2) 187.5 kg s^–1

(3) 185.5 kg s^–1

(4) 137.5 kg s^–1

If a person with a spring balance and a body hanging from it goes up and up in an aeroplane, then the reading of the weight of the body as indicated by the spring balance will 

(1) Go on increasing

(2) Go on decreasing

(3) First increase and then decrease

(4) Remain the same

A body is imparted motion from rest to move in a straight line. If it is then obstructed by an opposite force, then:

(1) The body may necessarily change direction

(2) The body is sure to slow down

(3) The body will necessarily continue to move in the same direction at the same speed

(4) None of these

Two balls of masses m₁ and m₂ are separated from each other by a powder charge placed between them. The whole system is at rest on the ground. Suddenly the powder charge explodes and masses are pushed apart. The mass m₁ travels a distance s₁ and stops. If the coefficients of friction between the balls and ground are same, the mass m₂ stops after travelling the distance 

(1) $s_2=\frac{m_1}{m_2}{s}_1$

(2) $s_2=\frac{m_2}{m_1}{s}_1$

(3) $s_2=\frac{m_1^2}{m_2^2}{s}_1$

(4) $s_2=\frac{m_2^2}{m_1^2}{s}_1$

A force vector applied on a mass is represented as $\overrightarrow{F}=6\hat{i}-8\hat{j}+10\hat{k}$ and accelerates with 1 m/s². What will be the mass of the body?

(1) $10\sqrt{2}kg$

(2) $2\sqrt{10}kg$

(3) 10 kg

(4) 20 kg

A cricket ball of mass 250 g collides with a bat with velocity 10 m/s and returns with the same velocity within 0.01 second. The force acted on bat is 

(1) 25 N

(2) 50 N

(3) 250 N

(4) 500 N

A pendulum bob of mass 50 gm is suspended from the ceiling of an elevator. The tension in the string if the elevator goes up with uniform velocity is approximately 

(1) 0.30 N

(2) 0.40 N

(3) 0.42 N

(4) 0.50 N

The average force necessary to stop a bullet of mass 20 g moving with a speed of 250 m/s, as it penetrates into the wood for a distance of 12 cm is 

(1) 2.2 × 10³ N

(2) 3.2 × 10³ N

(3) 4.2 × 10³ N

(4) 5.2 × 10³ N

A man measures time period of a pendulum (T) in stationary lift. If the lift moves upward with acceleration $\frac{g}{4},$ then new time period will be 

(1) $\frac{2T}{\sqrt{5}}$

(2) $\frac{\sqrt{5}T}{2}$

(3) $\frac{\sqrt{5}}{2T}$

(4) $\frac{2}{\sqrt{5}T}$

If rope of lift breaks suddenly, the tension exerted by the surface of lift (a = acceleration of lift) 

(1) mg

(2) m(g + a)

(3) m(g – a)

(4) 0