Question

A body of mass m is approaching towards the centre of a hypothetical hollow planet of mass M and radius R. The speed of the body when it passes the centre of the planet through its diametrical chute is

• A. $\sqrt { \frac { G M } { R } }$
• B. $\sqrt { \frac { 2 G M } { R } }$
• C. Zero
• D. None of these.

Answer 1

Answer: (B)

$\sqrt { \frac { 2 G M } { R } }$

Answer 2

At infinity the total energy of the body is zero. Therefore the total energy of the body just before hitting the planet of P will be zero according to the conservation of energy

⇒ F_p =E_∞ = 0

⇒ U_p + K_p = 0

⇒ - $\frac { \mathrm { GMm } } { \mathrm { R } } + \frac { 1 } { 2 }$ mv² = 0

⇒ v = .

Since the force imparted on a particle inside spherical shell is

zero, therefore the velocity of the particle inside the spherical

shell remain constant. Therefore, the body passes the centre of

the planet with same speed v = $\sqrt { \frac { 2 \mathrm { GM } } { \mathrm { R } } }$ .