Question

A small ball of mass 'm' is released at a height 'R' above the earth surface, as shown in the given figure. The maximum depth of the ball to which it goes is R/2 inside the earth through a narrow groove before coming to rest momentarily. The groove, contains an ideal spring of spring constant k and natural length R. The value of k, if R is the radius of earth and M mass of earth, is –

• A.
• B. $\frac { 6 \mathrm { GMm } } { \mathrm { R } ^ { 3 } }$
• C. $\frac { 9 \mathrm { GMm } } { \mathrm { R } ^ { 3 } }$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

By conservation of mechanical energy

– $\frac { 6 \mathrm { mM } } { 2 \mathrm { R } } = - \frac { \mathrm { G } ( \mathrm { m } ) ( \mathrm { M } ) } { ( \mathrm { R } / 2 ) } + \frac { 1 } { 2 } \mathrm { k } \left( \frac { \mathrm { R } } { 2 } \right) ^ { 2 }$