Question

When an athlete runs with some acceleration, he leans forward. The line joining his centre of mass to his foot which is in contact with the ground makes an angle θ with the vertical. The coefficient of friction between his foot and the ground is k. His foot does not slip on the ground. His acceleration is 

(a) kg 

(b) kgtan θ 

(c) gtan θ

(d) (gtan θ)/k

Answer 1

Correct Answer is: (c) gtan θ

C = centre of mass.

Taking torques about C, 

F θ OCcos θ = N x OCsin θ

or F = mgtan θ  = ma

or a = gtan θ .