Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

A spherical planet has a mass $M_p$ and diameter $D_p$ . A particle of mass $m$ falling freely near the surface of this planet will experience acceleration due to gravity equal to:

$\frac{4GM_pm}{D_p^2}$

$\frac{4GM_p}{D_p^2}$

$\frac{GM_pm}{D_p^2}$

$\frac{GM_p}{D_p^2}$

Step-by-Step Solution

Formula for Acceleration Due to Gravity: The acceleration due to gravity ( $g$ ) on the surface of a planet with mass $M_p$ and radius $R_p$ is derived from Newton's Law of Universal Gravitation. The gravitational force on a mass $m$ is $F = \frac{GM_p m}{R_p^2}$ . By Newton's second law, force $F = mg$ . Therefore, the acceleration is $g = \frac{F}{m} = \frac{GM_p}{R_p^2}$ [Equation 7.9].
Substitute Diameter: The problem provides the diameter $D_p$ . The radius is half the diameter: $R_p = \frac{D_p}{2}$ .
Calculation: Substitute $R_p$ into the equation for $g$ : $g = \frac{GM_p}{(D_p/2)^2} = \frac{GM_p}{D_p^2 / 4} = \frac{4GM_p}{D_p^2}$ Note that acceleration due to gravity is independent of the mass of the falling particle ( $m$ ).

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