Question

A metal ball of specific gravity $4.5$ and specific heat $0.1cal/g{m}^{\circ }C$ is placed on a large slab of ice at $0^{\circ }C$. Half of the ball sinks in the ice. The initial temperature of the ball is

• A. ${100}^{\circ }C$
• B. ${90}^{\circ }C$
• C. ${80}^{\circ }C$
• D. ${70}^{\circ }C$

Answer 1

Answer: (C)

${80}^{\circ }C$

Specific gravity of ice is $0.9$.

Let the Volume of ice melted be $V$, the its mass is $m=0.9V\times 1000$.

The mass of metal ball twice of the submerged mass in ice, equal to $m_2=2\times 4.5\times V\times 1000=10m$

Now, balancing the heat,

$10m\times 0.1\times \Delta T=mL;L=80cal/g$

$\Rightarrow \Delta T={80}^{o}C$