A particle of mass 0.3 kg is subjected to a force F = –kx with k = 15 N/m. What will be its initial acceleration if it is released from a point 20 cm away from the origin

(1) 5 m/s²

(2) 10 m/s²

(3) 3 m/s²

(4) 15 m/s²

An elevator weighing 6000 kg is pulled upward by a cable with an acceleration of 5 ms^–2. Taking g to be 10 ms^–2, then the tension in the cable is 

(1) 6000 N

(2) 9000 N

(3) 60000 N

(4) 90000 N

The ratio of the weight of a man in a stationary lift and when it is moving downward with uniform acceleration ‘a’ is 3 : 2. The value of ‘a’ is (g-Acceleration due to gravity of the earth) 

1. $\frac{3}{2}g$

2. $\frac{g}{3}$

3. $\frac{2}{3}g$

4. g

If force on a rocket having exhaust velocity of 300 m/sec is 210 N, then rate of combustion of the fuel is 

(1) 0.7 kg/s

(2) 1.4 kg/s

(3) 0.07 kg/s

(4) 10.7 kg/s

In an elevator moving vertically up with an acceleration g, the force exerted on the floor by a passenger of mass M is:

(1) Mg

(2) $\frac{1}{2}Mg$

(3) Zero

(4) 2 Mg

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