Question

A rigid rod of length 1 m is resting at an angle $\theta ={45}^o$ as shown in the figure. The end P is dragged with a velocity of U=5 m/s on the right.
At the instant shown, the magnitude of the velocity V(in m/s) of point Q as it moves along the wall without losing contact is

• A. 5
• B. 6
• C. 8
• D. 10

Answer 1

The correct option is A 5


$V_P=r_P\omega$

$\Rightarrow 5=1\times sin{45}^o\times \omega$
$\Rightarrow \omega =\frac{5}{1\times {45}^o}$(rad/s); anticlockwise

$V_Q=r_Q\omega$

$\Rightarrow V_Q=1\times cos{45}^o\times \frac{5}{1\times {45}^o}$
$=5m/s$

AVOID MISTAKE

$V_P=IQ\times \omega$

$5=1cos{45}^o\times \omega$

$\omega =\frac{5}{cos{45}^o}$

$V_Q=IP\times \omega$

$=1sin{45}^o\times \frac{5}{cos{45}^o}$

$=\frac{5}{tan{45}^o}=5m/s$

Note: Here student gets right answer by chance, (because $\angle ={45}^o$)because, we should take distance perpendicular to velocity, not parallel, so

$V_P=IP\times =r_P\times \omega$

and $V_Q=IQ\times =r_Q\times \omega$