Question

What should be the angular velocity of earth about its own axis so that the weight of the body at equator would become $\frac { 3 } { 4 }$th of its present value-

• A. $\frac { 1 } { 400 }$ rad/s
• B. $\frac { 1 } { 800 }$ rad/s
• C. $\frac { 1 } { 1600 }$ rad/s
• D. $\frac { 1 } { 3200 }$ rad/s

Answer 1

Answer: (C)

$\frac { 1 } { 1600 }$ rad/s

Answer 2

Wt. = $\frac { 3 } { 4 }$ of weight so

g_eff = $\frac { 3 } { 4 }$g

at equator

g_eff = g – Rw² = $\frac { 3 } { 4 }$g

w = $\frac { 1 } { 2 }$ × $\frac { 1 } { 800 }$

= $\frac { 1 } { 1600 }$ rad/s