The value of g at a particular point is 9.8 ms-2. Suppose theearth suddenlyshrinks uniformly to half its present size without losing any mass. The value ofg at the same point (distance of the point from the centre of earth does not change) will now be

Question

The value of g at a particular point is 9.8 ms-2. Suppose theearth suddenlyshrinks uniformly to half its present size without losing any mass. The value ofg at the same point (distance of the point from the centre of earth does not change) will now be (A) 9.8 ms-2 (B) 4.9 ms-2 (C) 19.6 ms-2 (D) 39.2 ms-2

Tardigrade Admin · Accepted Answer

If gi be the initial value tor acceleration aue to gravity and gf, be the final value then gi=(G M/R2)=g and gf=(G M/((R)2+(R)2)2=g <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/c85fa029c98555a791c4819a3dc12e7e-.png" />

Q. The value of g at a particular point is $9.8 m s^{- 2}$ . Suppose theearth suddenlyshrinks uniformly to half its present size without losing any mass. The value ofg at the same point (distance of the point from the centre of earth does not change) will now be

$9.8 m s^{- 2}$

$4.9 m s^{- 2}$

$19.6 m s^{- 2}$

$39.2 m s^{- 2}$

If $g_{i}$ be the initial value tor acceleration aue to gravity and $g_{f}$ , be the final value then
$g_{i} = \frac{GM}{R ^{2}} = g$ and
$g_{f} = \frac{GM}{( \frac{R}{2} + \frac{R}{2} ) ^{2}} = g$

Q. The value of g at a particular point is 9.8ms−2. Suppose theearth suddenlyshrinks uniformly to half its present size without losing any mass. The value ofg at the same point (distance of the point from the centre of earth does not change) will now be

9.8ms−2

4.9ms−2

19.6ms−2

39.2ms−2