Question

Q.17 During motion of a man from equator to pole of earth , its weight will ( neglect the effect of change in the radius of earth ) (1) increase by 0.34 % (2) Decrease by 0.34 % (3) Increase by 0.52 % (4) Decrease by 0.52 %

Answer 1

T = time period of rotation of earth = 24 hours = 24 x 3600 sec = 86400 sec

w = angular velocity of rotation of earth = 2π/T = 2(3.14)/86400 = 7.3 x 10⁻⁵ rad/s

R = radius of earth = 6.4 x 10⁶ m

m = mass of earth

at equator , acceleration due to gravity is given as

g₁ = g - R w²

g₁ = 9.8 - (6.4 x 10⁶) (7.3 x 10⁻⁵)²

g₁ = 9.766 m/s²

weight at equator is given as

W₁ = m g₁

at pole , acceleration due to gravity is given as

g₂ = g

g₂ = 9.8

weight at pole is given as

W₂ = m g₂

Percentage change in weight is given as

%age change = (W₂ - W₁) x 100/W₁ = (mg₂ - mg₁) x 100/(mg₁)

%age change = (9.8 - 9.766) x 100/(9.766) = 0.34%

hence the correct choice is

(1) increase by 0.34 %