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A planet of radius R has an acceleration due to gravity of g_(s) on its surface. A deep smooth tunne is dug on this planet, radially inward, to reach a point P located at a distance of (R)/(2) from the centre of the planet. Assume that the planet has uniform density. The kinetic energy required to be given to a small body of mass m, projected radially outward from P, so that it gains a maximum altitude equal to the thrice the radius of the planet from its surface, is equal to (##DSH_NTA_JEE_MN_PHY_C07_E03_017_Q01.png" width="80%"> |
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Answer» `(63)/(16)mg_(s) R ` `V(x) = {{: (- g_(s) R((3)/(2) - (1)/(2)(x^(2))/(R^(2)) ), " when " x lt R),(-g_(s)R((R)/(x)), " when " x gt R):}}` The energy required to project the body to a MAXIMUM altitude of 3 R from its surface , is `m (V_(B) | x = (R)/(2) - V_(p) | x =4 R ) = (9)/(8) mg_(s)R.` |
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