Ncert Exercises & Solutions

Show that a force that does no work must be a velocity-dependent force.

Hint: The force and the velocity should always be perpendicular to each other.

Step 1: Let no work is done by a force, so we have,

dW = F.dl = 0

\Rightarrow

$\Rightarrow$ F.vdt = 0 (Since. dl = vdt and dt

\neq

$\neq$ 0)

\Rightarrow

$\Rightarrow$ F.v = 0

Step 2: Thus, F must be velocity dependent which implies that angle between F and v is 90

°

$°$ . If v changes (direction), then (directions) F should also change so that the above condition is satisfied.