# A ball is thrown upward near the surface of the earth with a velocity of 50 m/s. After 5 s later its velocity becomes zero momentarily. If the ball were thrown up with the same velocity on Planet...

A ball is thrown upward near the surface of the earth with a velocity of 50 m/s. After 5 s later its velocity becomes zero momentarily. If the ball were thrown up with the same velocity on Planet X, after 5 s it would still be moving upwards at 31 m/s. (Neglect air resistance)

The ratio of the magnitude of the gravitational field intensity near the surface of planet X and the magnitude of the gravitational field intensity near the surface of the earth is equal to

[1] 0.16

[2] 0.38

[3] 0.53

[4] 0.63

[5] 1.59

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### 1 Answer

When the ball is thrown upward near the surface of the earth with a velocity of 50 m/s it comes to a halt after 5 seconds. On Planet X, when thrown with the same velocity it continues to move upwards at 31 m/s.

If the initial velocity of a particle is u and its acceleration is a, the final velocity after t seconds is v. The relation between the variables is v = u + a*t.

Let the ratio of the magnitude of the gravitational field intensity near the surface of planet X and the magnitude of the gravitational field intensity near the surface of the Earth be X; if the former is X*C, the latter is X

Using the data given in the problem,

31 = 50 - X*C*5, 0 = 50 - C*5

C*5 = 50

Substitute in 31 = 50 - X*C*5

=> 31 = 50 - 50*X

=> 50*X = 19

=> X = 0.38

The required ratio is 0.38.

**The correct answer is option 2.**