Question

A solid sphere of mass $0.1$ Kg and radius $2$ cm rolls down an inclined plane $1.4$ m in length (slope $1$ in $10$). Starting from rest its final velocity will be

• A. $1.4$ m/sec
• B. $0.14$ m/sec
• C. $14$ m/sec
• D. $0.7$ m/sec

Answer 1

The correct option is A $1.4$ m/sec

We have $tan\theta =\frac{1}{10}$
or
$\theta =0.099$
or
$sin\theta =0.099$
Thus height of the of incline is given as $0.099\times 1.4=0.14m$
Using conservation of energy we have
$mg\left(0.14\right)=\frac{1}{2}m{v}^2+\frac{1}{5}m{v}^2$
or
$0.14g=\frac{7}{10}{v}^2$
or
$v=\sqrt{\frac{0.14\times 9.81\times 10}{7}}$
or
$v=1.4m/s$