SATHEE: Gravitation Question 38

Gravitation Question 38

Question: What should be the velocity of earth due to rotation about its own axis so that the weight at equator become 3/5 of initial value. Radius of earth on equator is 6400 km [AMU 1999]

Options:

A) $[7.4 \times 10^{- 4}, r a d / \sec]$

B) $[6.7 \times 10^{- 4}, r a d / \sec]$

C) $[7.8 \times 10^{- 4}, r a d / \sec]$

D) $[8.7 \times 10^{- 4}, r a d / \sec]$

Show Answer

Answer:

Correct Answer: C

Solution:

Weight of the body at equator = $[\frac{3}{5}]$

of initial weight $[g^{'} = \frac{3}{5} g]$

(because mass remains constant) $[g^{'} = g - ω^{2} R \cos^{2} λ]$

Þ $[\frac{3}{5} g = g - ω^{2} R \cos^{2} (0^{\circ})]$

Þ $[ω^{2} = \frac{2 g}{5 R}]$

Þ $[ω = \sqrt{\frac{2 g}{5 R}} = \sqrt{\frac{2 \times 10}{5 \times 6400 \times 10^{3}}}]$ = $[7.8 \times 10^{- 4} \frac{r a d}{\sec}]$

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Gravitation Question 38

Question: What should be the velocity of earth due to rotation about its own axis so that the weight at equator become 3/5 of initial value. Radius of earth on equator is 6400 km [AMU 1999]

Options:

Answer:

Solution:

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