Question

An ice block is projected vertically up with a velocity $20m{s}^{-1}$. The amount of ice that melt when it reaches the ground assuming the loss of P.E. is converted into heat energy if the mass of ice block is $4.2kg$ initially.

• A. $2.5gm$
• B. $2.5kg$
• C. $0.25kg$
• D. $0.25gm$

Answer 1

The correct option is A $2.5gm$

R.E.F image

Since at the Maximum height

the velocity of the ice block

becomes It is because

the kinetic energy is converted

into the potential (low of conservation of mechanical energy)

$\Rightarrow$ gain in potential energy at max height $\Delta U=\frac{1}{2}m{v}^2=\frac{1}{2}\times 4.2\times 20\times 20$

$=840J$

Since all the penitential energy is covered into heat energy ($\Delta Q$) when block returns

to ground

$\Rightarrow \Delta Q=\Delta U$

now, If 'm' mass of ice block is melted

into water

$\Rightarrow \Delta Q=mL,$ $L\to$ latent heat of water

$\Rightarrow \Delta U=mL$

$\Rightarrow 840=m\times 3.4\times {10}^5$

$\Rightarrow m=\frac{840}{3.4\times {10}^5}kg$

$=\frac{840\times {10}^3}{3.4\times {10}^5}g$

$\Rightarrow m=2.47g\simeq 2.5g$