A force F acting on a body depends on its displacement s as F propto s-1 / 3 . The power delivered by F will depend on displacement as

Question

A force F acting on a body depends on its displacement s as F propto s-1 / 3 . The power delivered by F will depend on displacement as (A) s2/3 (B) s- 5/3 (C) s1/2 (D) s0

Tardigrade Admin · Accepted Answer

F propto s-1 / 3 i.e., acceleration a propto s- 1 / 3 or v( textd textitv/ textd textits)= textK textits- 1 / 3 text or textv2 propto texts2 / 3 or textitv propto textits1 / 3 Now textitP= textitF.v or textitP propto s- 1 / 3 text. textits1 / 3 text or textitP propto s0 i.e., power is independent of s.

Q. A force $F$ acting on a body depends on its displacement $s$ as $F \propto s^{- 1/3}$ . The power delivered by $F$ will depend on displacement as

$s^{2/3}$

$s^{- 5/3}$

$s^{1/2}$

$s^{0}$

$F \propto s^{- 1/3}$
i.e., acceleration $a \propto s^{- 1/3}$
or $v \frac{d v}{d s} = K s^{- 1/3} or$ $v^{2} \propto s^{2/3}$
or $v \propto s^{1/3}$
Now $P = F.v$
or $P \propto s^{- 1/3} . s^{1/3} or P \propto s^{0}$
i.e., power is independent of s.

Q. A force F acting on a body depends on its displacement s as F∝s−1/3 . The power delivered by F will depend on displacement as

s2/3

s−5/3

s1/2

s0