A balloon rises from rest with a constant acceleration g/8. A stone is released from it when it has risen to height h. The time taken by the stone to reach the ground is

(1) $4\sqrt{\frac{h}{g}}$

(2) $2\sqrt{\frac{h}{g}}$

(3) $\sqrt{\frac{2h}{g}}$

(4) $\sqrt{\frac{g}{h}}$ 

Two bodies are thrown simultaneously from a tower with same initial velocity v₀ : one vertically upwards, the other vertically downwards. The distance between the two bodies after time t is

(1) $2v_{0}t+\frac{1}{2}g{t}^2$

(2) 2v₀t

(3) $v_{0}t+\frac{1}{2}g{t}^2$

(4) v₀t

A body falls freely from the top of a tower. It covers 36% of the total height in the last second before striking the ground level. The height of the tower is:

(1) 50 m

(2) 75 m

(3) 100 m

(4) 125 m

A particle is projected upwards. The times corresponding to height \(h\) while ascending and while descending are t₁ and t₂ respectively. The velocity of projection will be:
1. \(gt_1\)
2. \(gt_2\)
3. \(g(t_1+t_2)\)
4. \(\frac{g(t_1+t_2)}{2}\)

A projectile is fired vertically upwards with an initial velocity u. After an interval of T seconds a second projectile is fired vertically upwards, also with initial velocity u.

(1) They meet at time $t=\frac{u}{g}$ and at a height $\frac{u^2}{2g}+\frac{g{T}^2}{8}$

(2) They meet at time $t=\frac{u}{g}+\frac{T}{2}$ and at a height $\frac{u^2}{2g}+\frac{g{T}^2}{8}$

(3) They meet at time $t=\frac{u}{g}+\frac{T}{2}$ and at a height $\frac{u^2}{2g}-\frac{g{T}^2}{8}$

(4) They never meet

Two cars are moving in the same direction with the same speed \(30\) km/hr. They are separated by a distance of \(5\) km. The speed of a car moving in the opposite direction, if it meets these two cars at an interval of \(4\) minutes, will be:
1. \(40\) km/hr
2. \(45\) km/hr
3. \(30\) km/hr
4. \(15\) km/hr

A 150 m long train is moving to north at a speed of 10 m/s. A parrot flying towards south with a speed of 5 m/s crosses the train. The time taken by the parrot the cross to train would be: 

(1) 30 s

(2) 15 s

(3) 8 s

(4) 10 s

A moves with 65 km/h while B is coming back of A with 80 km/h. The relative velocity of B with respect to A is 

1. 80 km/h

2. 60 km/h

3. 15 km/h

4.145 km/h

Two trains along the same straight rails moving with constant speed 60 km/hr and 30 km/hr respectively towards each other. If at time t = 0, the distance between them is 90 km, the time when they collide is:

1. 1 hr

2. 2 hr

3. 3 hr

4. 4 hr

A bus is moving with a velocity 10 m/s on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what velocity should the scooterist chase the bus

(1) 50 m/s

(2) 40 m/s

(3) 30 m/s

(4) 20 m/s