Find the minimum height of the obstacle so that the sphere can stay in equilibrium.

Question

Find the minimum height of the obstacle so that the sphere can stay in equilibrium. (A) ( R /1+ cos θ) (B) ( R /1+ sin θ) (C) R(1- sin θ) (D) R (1- cos θ)

Tardigrade Admin · Accepted Answer

The sphere is on the verge of topping when a line of action of weight passes through the edge. cos θ=(( R - h )/ R ) ⇒ h = R - R cos θ

Q. Find the minimum height of the obstacle so that the sphere can stay in equilibrium.

$\frac{R}{1 + c o s θ}$

$\frac{R}{1 + s i n θ}$

$R (1 - sin θ)$

$R (1 - cos θ)$

The sphere is on the verge of topping when a line of action of weight passes through the edge.
$cos θ = \frac{( R - h )}{R} \Rightarrow h = R - R cos θ$

Q. Find the minimum height of the obstacle so that the sphere can stay in equilibrium.

1+cosθR​

1+sinθR​

R(1−sinθ)

R(1−cosθ)

The sphere is on the verge of topping when a line of action of weight passes through the edge. cosθ=R(R−h)​⇒h=R−Rcosθ

$\frac{R}{1 + c o s θ}$

$\frac{R}{1 + s i n θ}$

$R (1 - sin θ)$

$R (1 - cos θ)$

The sphere is on the verge of topping when a line of action of weight passes through the edge.
$cos θ = \frac{( R - h )}{R} \Rightarrow h = R - R cos θ$