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

A monkey of mass 20kg is holding a vertical rope. The rope will not break when a mass of 25 kg is suspended from it but will break if the mass exceeds 25 kg. What is the maximum acceleration with which the monkey can climb up along the rope (g = 10 m/s²) 

(1) 10 m/s²

(2) 25 m/s²

(3) 2.5 m/s²

(4) 5 m/s²