Question

A dumbell consists of two identical small ball of mass $\frac{1}{2}Kg$ each connected to the two ends of a $50Cm$ long light rod. The dumb bell is rotating about a fixed axis through the centre of the road and perpendicular to it at an angular speed $10rad{s}^{-1}$. An impulsive force of average magnitude $5N$ acts on one of the masses in the direction of its velocity for $0.1s$. Find the angular velocity of the system.

• A. $10rad{s}^{-1}$
• B. $12rad{s}^{-1}$
• C. $8rad{s}^{-1}$
• D. $14rad{s}^{-1}$

Answer 1

The correct option is D $14rad{s}^{-1}$

$\therefore V=rw$

$=\frac{25}{100}\times 10$

$=2.5m/s$

$\int \overrightarrow{F}.\overrightarrow{d}t=m{V}_f-m{V}_i$

$\therefore \left(0.1\right)\left(5_{=}\right(0.5\left)\right[V_f-2-5]$

$V_f=3.5$

$V_f=r{w}_f$

$3.5=\frac{25}{100}{w}_f$

$w_f=14rad/sec$