It is a well-known fact that during a total solar eclipse the disk of the moon almost completely covers the disk of the sun. The distance of moon (r_ME) and sun (r_SE) from the earth surface is 3.84 x 10⁸ m and 1.496 x 1011 m while the diameter of Sun is 1.390 x 10⁹ m. Determine the approximate diameter of the moon.

State which of the following situations are possible and give an example for each of these?
(a) An object with a constant acceleration but with zero velocity.
(b) An object moving in a certain direction with acceleration in the perpendicular direction.

A body is projected vertically upwards from A, the top of a tower it reaches the ground in it t₁ second.If it is projected vertically downwards from A with the same velocity it reaches the ground in t₂ second.If it falls freely, from A, prove that it would reach the ground in \(\sqrt { { t }_{ 1 }{ t }_{ 2 } } \) second.

The maximum height attained by a projectile is increased by 10% by increasing its speed of projection, without changing the angle of projection. What will the percentage increase in the horizontal range?

The range of a rifle bullet is 1000m, when \(\theta \) is the angle of projection. If the bullet is fired with the same angle from a car travelling at 36km/h towards the target, show that the range will be increasing by 142.9\(\sqrt { tan\theta m } \).
When the bullet is fired from the moving car, the horizontal component velocity of the bullet increases with the velocity of car. But the vertical component of the velocity remains uneffected.

You may have seen in a circus a motorcyclist driving in vertical loops inside a death well (a hollow spherical chamber with holes, so the spectators can watch from outside). Explain clearly, why the motorcyclist does not drop down when he is at the uppermost point, with no support from below. What is the minimum speed required at the uppermost position to perform a vertical loop if the radius of the chamber is 25 m?

Calculate the change in the energy of a 500 kg astellite when it falls from an altitude of 200 km to 199km.If this change takes place during one orbit.Calculate the retarding force on the satellite Given,mass of the earth = \(6\times { 10 }^{ 24 }kg\)  and radius of the earth = 6400 km

The brass scale of a barometer gives correct reading at 0 ⁰C. Coefficient of linear expansion of brass is 2.0 x 10^-5/⁰ C. The barometer reads 75.00 cm at 27⁰ C. What is the true atmospheric pressure at 27⁰ C.

Calculate the total number of degrees of freedom possessed by the molecules in 1cm³ of H₂ gas at temperature 273k and 1 atm pressure?