A very large number of balls are thrown vertically upwards in quick successions in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is 5 m, the number of balls thrown per minute is (take g = 10 m/s²)

• 80

• 120

• 40

• 60

2.

The resultant of two forces, one double the other in magnitude, is perpendicular to the smaller of the two forces. The angle between the two forces is

• 120°

• 60°

• 90°

• 150°

A projectile is moving at 20 ms^-1 at its highest point, where it breaks into equal parts due to an internal explosion. One part moves vertically up at 30 ms^-1 with respect to the ground. Then the other part will move at

• 20 ms^-1

• $10\sqrt{31} {\mathrm{ms}}^{-1}$

• 50 ms^-1

• 30 ms^-1

A body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is

• R/2

• R/3

• R/5

• R/4

From the top of a tower a stone is thrown up which reaches the ground in a time t₁. A second stone thrown down with the same speed reaches the ground in a time t₂. A third stone released from rest from the same between reaches the ground in a time t₃. Then

• $\frac{1}{{\mathrm{t}}_3} = \frac{1}{{\mathrm{t}}_2} - \frac{1}{{\mathrm{t}}_1}$

• ${\mathrm{t}}_3^2 = {\mathrm{t}}_1^2 - {\mathrm{t}}_2^2$

• ${\mathrm{t}}_3 = \frac{{\mathrm{t}}_1 + {\mathrm{t}}_2}{2}$

• ${\mathrm{t}}_3 = \sqrt{{\mathrm{t}}_1 {\mathrm{t}}_2}$

The energy spectrum of a black body exhibits a maximum around a wavelength λ₀. The temperature of the black body is now changed such that the energy is maximum around a wavelength $\frac{3{\mathrm{\lambda }}_0}{4}$. The power radiated by the black body will now increase by a factor of

• 64/27

• 256/81

• 4/3

• 16/9

n identical bulbs, each designated to draw a power P from a certain voltage supply. The total power which they will draw is

• $\frac{\mathrm{P}}{\mathrm{n}}$

• $\frac{\mathrm{P}}{{\mathrm{n}}^2}$

• nP

• P

A racing car moving towards a cliff, sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If v is the velocity of sound, then the velocity of the car is

• v/2

• $\mathrm{v}/\sqrt{2}$

• v/4

• v/3

A railway engine whistling at a constant frequency moves with a constant speed. It goes past a stationary observer beside the railway track. Which of the following graphs best represent the variation of frequency of the sound n heard by the observer with the time t ?

The tension of a stretched string is increased by 69 %. In order to keep its frequency of vibration constant, its length must be increased by

• 30 %

• 20 %

• 69 %

• $\sqrt{69} \%$