A tourist of mass is travelling upward in a space-elevator car

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

A tourist of mass

60\,\text{kg}

is travelling upward in a space-elevator car. When the car is

4.0\,\text{km}

above the Earth’s surface it is slowing down with an acceleration of

1.5\,\text{m\,s}^{-2}

directed downward. Take

g

at the surface as

9.80\,\text{m\,s}^{-2}

and Earth’s radius

R = 6.4\times10^{6}\,\text{m}

. (i) Using a suitable approximation for

h\ll R

, compute the value of

g

at the given height. (ii) Calculate the apparent weight of the tourist at that instant using the value of

g

obtained in part (i). (iii) If, instead, the value

g = 9.80\,\text{m\,s}^{-2}

were (incorrectly) used in the calculation, find the apparent weight that would be reported. (iv) Determine the percentage error introduced by using

9.80\,\text{m\,s}^{-2}

instead of the actual value of

g