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

A plumb line is suspended from a ceiling of a car moving with horizontal acceleration of a. What will be the angle of inclination with vertical 

1. tan^–1(a/g)

2. tan^–1(g/a)

3. cos^–1(a/g)

4. cos^–1(g/a)

A body of mass 2 kg has an initial velocity of 3 meters per second along OE and it is subjected to a force of 4 N in a direction perpendicular to OE. The distance of the body from O after 4 seconds will be 

(1) 12 m

(2) 20 m

(3) 8 m

(4) 48 m

A block of mass m is placed on a smooth wedge of inclination θ. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block (g is acceleration due to gravity) will be 

(1) $mg \cos \theta$

(2) $mg \sin \theta$

(3) mg

(4) $mg/\cos \theta$

The linear momentum p of a body moving in one dimension varies with time according to the equation p = a + bt² where a and b are positive constants. The net force acting on the body is 

(1) A constant

(2) Proportional to t²

(3) Inversely proportional to t

(4) Proportional to t