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

A lift of mass 1000 kg is moving with an acceleration of 1 m/s² in the upward direction. Tension developed in the string, which is connected to the lift, is:

(1) 9,800 N

(2) 10,000 N

(3) 10,800 N

(4) 11,000 N

A lift accelerated downward with acceleration 'a'. A man in the lift throws a ball upward with acceleration a₀ (a₀ < a). Then acceleration of ball observed by an observer, which is on earth, is 

(1) (a + a₀) upward

(2) (a – a₀) upward

(3) (a + a₀) downward

(4) (a – a₀) downward

A lift is moving down with acceleration a. A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively 

(1) g, g

(2) g – a, g – a

(3) g – a , g

(4) a, g