A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?

The Vernier constant of Vernier callipers is 0.1 mm and it has zero error of ($$-$$0.05) cm. While measuring diameter of a sphere, the main scale reading is 1.7 cm and coinciding vernier division is 5. The corrected diameter will be _________ $$\times$$ 10^$$-$$2 cm.

A small spherical ball of radius 0.1 mm and density 10⁴ kg m^$$-$$3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h will be ___________ m.

(Given g = 10 ms^$$-$$2, viscosity of water = 1.0 $$\times$$ 10^$$-$$5 N-sm^$$-$$2).

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms^$$-$$1. The third resonance is observed when the air column has a length of _____________ cm.