Motion in A Plane

When a low flying aircraft passes over head, we sometimes notice a slight shaking of the picture on our TV screen. This is due to 

• diffraction of the signal received from the antenna

• interference of the direct signal received by the antenna with the weak signal reflected by the passing aircraft

• change ofmagenetic flux occuring due to the passage of aircraft

• vibration created by the passage of aircraft

The maximum height attained by a projectile when thrown at an angle θ with the horizontal is found to be half the horizontal range. Then θ is equal to

• tan^-1 (2)

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{4}$

• ${\tan }^{-1} \left(\frac{1}{2}\right)$

A body is projected vertically upwards. The times corresponding to height h while ascending and while descending are t₁ and t₂ respectively. Then the velocity of projection is (g is acceleration due to gravity)

• $\mathrm{g}\sqrt{{\mathrm{t}}_1{\mathrm{t}}_2}$

• $\frac{{\mathrm{gt}}_1{\mathrm{t}}_2}{{\mathrm{t}}_1 + {\mathrm{t}}_2}$

• $\frac{\mathrm{g}\sqrt{{\mathrm{t}}_1{\mathrm{t}}_2}}{2}$

• $\frac{\mathrm{g}\left({\mathrm{t}}_1 + {\mathrm{t}}_2\right)}{2}$

A mass of 10 kg is suspended from a spring balance. It is pulled aside by a horizontal string so that it makes an angle of 60° with the vertical. The new reading of the balance is

• 20 kg-wt

• 10 kg-wt

• $10\sqrt{3} \mathrm{kg}-\mathrm{wt}$

• $20\sqrt{3} \mathrm{kg}-\mathrm{wt}$

The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y = 8t − 5t² m and x = 6t m, where t is in seconds. The velocity with which the projectile is projected is

• 6 ms^-1

• 8 ms^-1

• 10 ms^-1

• 14 ms^-1

A person throws balls into air vertically upward in regular intervals of time of one second. The next ball is thrown when the velocity of the ball thrown earlier becomes zero. The height to which the balls rise is (Assume, g = 10 ms^-2)

• 20 m

• 5 m

• 10 m

• 7.5 m

A projectile is projected at 10 ms^-1 by making at an angle 60° to the horizontal. After some time its velocity makes an angle of 30° to the horizontal. Its speed at this instant is

• $\frac{10}{\sqrt{3}}$

• $10\sqrt{3}$

• $\frac{5}{\sqrt{3}}$

• $5\sqrt{3}$

A stone is thrown vertically at a speed of 30 ms^-1 taking an angle of 45° with the horizontal. What is the maximum height reached by the stone ? Take g = 10 ms^-2.

• 30 m

• 22.5 m

• 15 m

• 10 m

An aeroplane executes a horizontal loop at a speed of 720 km/h with its wings banked at 45°. What is the radius of the loop ? Take g = 10 ms^-2

• 4 km

• 4.5 km

• 7.2 km

• 2 km

Which of the following is not a vector quantity ?

• Weight

• Nuclear spin

• Momentum

• Potential energy