Question

A machine which is $75$% efficient uses $12$ joules of energy in lifting up a $1$ kg mass through a certain distance. The mass is then allowed to fall through that distance. The velocity at the end of its fall is(in $m{s}^{-1}$):

• A. $\sqrt{24}$
• B. $\sqrt{32}$
• C. $\sqrt{18}$
• D. $\sqrt{9}$

Answer 1

The correct option is C $\sqrt{18}$

If $100$ joules is given in the machine and $75$ joules is output

So, If $12$ joules is given in the machine and $\frac{75}{100}\times 12=9$ joules is output

$w=f\times d$

$9=1\times 9.8\times d$

$\frac{9}{9.8}=d$

$v^2=u^2+2as$

$2as=2\times 9.8\times \frac{9}{9.8}=18$

$v^2=18$

$v=\sqrt{18}\frac{m}{s}$