Question

Let F be the force acting on a particle having position vector r and $\tau$ be the torque of this force about the origin. Then,

• A. $r.\tau$ = 0 and $F.\tau \ne 0$
• B. $r.\tau \ne 0$ and $F.\tau =0$
• C. $r.\tau \ne 0$ and $F.\tau \ne 0$
• D. $r.\tau$ = 0 and $F.\tau =0$

Answer 1

The correct option is D $r.\tau$ = 0 and $F.\tau =0$

torgue is the cross product of the force F and the position vector'r'

$\tau =r\times F$

so the angle between$\tau$ and F is ${90}^0$ and between $\tau$ and r is ${90}^0$

for example if we take dot product between two vectors as $\theta ={90}^0⟹cos\theta =cos{90}^0=0$ $⟹r.\tau =0$

$F.\tau =0$