Question

A mass 'm' suspended from a spring stretches it by 5cm when on the surface of the earth. The mass is then taken on to a height of 1600 km above earth's surface and again suspended from the same spring. At this altitude the extension of the spring is ______.

(Radius of earth = 6400 km)

विकल्प

• 3.2 cm

• 1.6 cm

• 6.4 cm

• 0.8 cm

Answer 1

A mass 'm' suspended from a spring stretches it by 5cm when on the surface of the earth. The mass is then taken on to a height of 1600 km above earth's surface and again suspended from the same spring. At this altitude the extension of the spring is 3.2 cm.

Explanation:

`g="GM"/r^2`

`thereforeg^'/g=r^2/(r'^2)`

R = 6400 km, r' = 6400 + 1600 = 8000 km

`g^'/g=(6400/8000)^2=(4/5)^2=16/25`

`W^'/W=(mg^')/(mg)=16/25`

Extension 'e' is proportional to weight

`e^'/e=16/25`

`thereforee^'=16/25xxe=16/25xx5=3.2  "cm"`