Question

A hammer of mass 1$kg$ having speed of 50$m/s$ , hit a iron nail of mass 200$gm$ . If specific heat of iron is 0.105 cal/gm'C and half the energy is converted into heat, the raise in temperature of nail is

• A. ${7.1}^{\circ }C$
• B. ${9.2}^{\circ }C$
• C. ${10.5}^{\circ }C$
• D. ${12.1}^{\circ }C$

Answer 1

Answer: (A)

${7.1}^{\circ }C$

It is known that $W=JQ$

Putting Values according to question:

$W=JQ\Rightarrow \frac{1}{2}\left(\frac{1}{2}M{v}^2\right)=J(m.c.\Delta \theta )$

$\Rightarrow \frac{1}{4}\times 1\times (50{)}^2=4.2[200\times 0.105\times \Delta \theta ]\Rightarrow \Delta \theta ={7.1}^{\circ }C$