A cow is tied to a post by a rope. The cow moves along the circular path always keeping the rope tight. If it describes 44 metres, when it has traced out 72° at the centre, the length of the rope is

Question

A cow is tied to a post by a rope. The cow moves along the circular path always keeping the rope tight. If it describes 44 metres, when it has traced out 72° at the centre, the length of the rope is (A) 35 metres (B) 22 metres (C) 56 metres (D) 45 metres

Tardigrade Admin · Accepted Answer

Length of arc =2 π r × (θ/360°) ⇒ 44=2 × (22/7) × r × (72/360) ⇒ r=(44 × 7 × 5/44)=35 m which is the length of the rope.

Q. A cow is tied to a post by a rope. The cow moves along the circular path always keeping the rope tight. If it describes $44 m e t res$ , when it has traced out $7 2^{\circ}$ at the centre, the length of the rope is

$35 m e t res$

$22 m e t res$

$56 m e t res$

$45 m e t res$

Length of arc $= 2 π r \times \frac{θ}{36 0 ^{\circ}}$
$\Rightarrow 44 = 2 \times \frac{22}{7} \times r \times \frac{72}{360}$
$\Rightarrow r = \frac{44 \times 7 \times 5}{44} = 35 m$
which is the length of the rope.

Q. A cow is tied to a post by a rope. The cow moves along the circular path always keeping the rope tight. If it describes 44metres, when it has traced out 72∘ at the centre, the length of the rope is

35metres

22metres

56metres

45metres