Question

At a certain point the potential energy and kinetic energy of a body of mass 0.1 kg moving vertically up are 3.6 J and 6.2 J. It rises to a maximum height of :

• A. 0.1 m
• B. 1 m
• C. 10 m
• D. 100 m

Answer 1

Answer: (C)

10 m

Given,

$P.E=3.6J$

$K.E=6.2J$

$g=9.8m/s^2$

$m=0.1kg$

Potential energy,

$P.E=mgh=3.6J$

$h=\frac{3.6}{0.1\times 9.8}=3.67m$

Kinetic energy,

$K.E=\frac{1}{2}m{v}^2=6.2J$

$v^2=\frac{6.2\times 2}{0.1}$

$v^2=124$

3rd equation of motion,

$v^2-u^2=-2hg$

$124-u^2=-9.8\times 3.67\times 2$

$u^2=194.56$ (initial velocity)

For maximum height, $v=0m/s$

$v^2-u^2=-2h_{m}g$

$h_m=\frac{194.56}{2\times 9.8}$

$h_m=10m$

The correct option is C.