Question

A stationary object at $4^{o}C$ weighing 3.5 kg falls from a height 2000 m on a snow mountain at $0^{o}C.$ If the temperature of the object before comes to rest immediately (g = 10 $m/s^2$ ) and latent heat of ice $=3.5\times {10}^{6}J/s),$ then the object :

• A. $2gm$ of ice
• B. $200gm$ of ice
• C. $20gm$ of ice
• D. $2kg$ of ice

Answer 1

The correct option is B $200gm$ of ice

Law of conservation of energy is valid.

Potential energy is the energy possessed by a body due to its weight. It is given by $PE=mgh$

where, m is mass, g is acceleration due to gravity and h is height.

This potential energy is utilized is giving latent heat to ice $m^{\prime }L=mgh$

Given $m=3.5kg,g=10m/s^2,h=2000m$

$L=3.5\times {10}^{5}J/s$

$m=\frac{mgh}{L}$

$m=\frac{3.5\times 10\times 2000}{3.5\times {10}^5}$

$m=0.2kg$ of ice

Also, $1kg={10}^{3}g$

$m=200g$ of ice.