The condition for a uniform spherical mass 'm' of radius 'r', to be a black hole is ______________.

[G = gravitational constant and g = acceleration due to gravity]

If the acceleration due to gravity is 'g' on the surface of Earth, then the value of acceleration due to gravity at a height of 32 km above the surface of Earth is (radius of Earth = 6400 km)

An alien is celebrating his 4^th birthday on his home planet, which is at a distance of 4 AU from the sun. What is the age of the alien in terrestrial years?

Weight of a body of mass decreases by 1% when it is raised to height 'h' above Earth's surface. If the body is taken to a depth 'h' in a mine, the change in its weight is

Directions: In the following question, a statement of Assertion is given, followed by a corresponding statement of Reason. Mark the correct answer as:

(a) If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.

(b) If both Assertion and Reason are true, but the Reason is not the correct explanation of the Assertion.

(c) If Assertion is true, but Reason is false.

(d) If both Assertion and Reason are false.

Assertion: The earth is slowing down and as a result the moon is coming nearer to it.

Reason: The angular momentum of the earth-moon system is not conserved.

Two spheres of masses 'm' and 'M' are situated in air and the gravitational force between them is 'F'. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be

A river is flowing from West to East with a speed of 5 m/min. A man can swim in still water with a velocity of 10 m/min. In which direction should the man swim, so as to take the shortest possible path to go to South?

A body thrown vertically upwards reaches a height and comes back. Which of the following is true about the acceleration due to gravity?

A body moving along the circular path of radius `R` describes an angle of 60o at the center of the circle, while moving from A to B. The displacement of the body is

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

A boatman can row with a speed of 10 kmh^–1. If a river of width 2 km flows at 5 kmh^–1, then what is the direction in which the boatman should row to reach a point on the other bank directly opposite to the point from where he started?

A mass of 2 kg is whirled in a horizontal circle by means of a string at an initial speed of 5 revolutions per minute. Keeping the radius constant the tension in the string is doubled. The new speed is nearly

The required emf of the cell E so as to show null deflection in voltmeter V connected across A and B of the circuit shown in the figure must be [cell and voltmeter are ideal]