Question

What is rise in temperature of a collective drop when initially $1gm$ and $2gm$ drops travel with velocities $10cm/sec$ and $15cm/sec$.

• A. $6.6\times {10}^{-3}{}^{\circ }C$
• B. $66\times {10}^{-3}{}^{\circ }C$
• C. $660\times {10}^{-3}{}^{\circ }C$
• D. ${66}^{\circ }C$

Answer 1

The correct option is B $66\times {10}^{-3}{}^{\circ }C$

momentum is conserved.

$1\times 10+2\times 15=3\times v$

$v=\frac{40}{3}$

Change in Kinetic Energy

$\Delta k=\frac{1}{2}\times 1\times (10{)}^2+\frac{1}{2}\times 2\times (15{)}^2-\frac{1}{2}\times 3{\left(\frac{40}{3}\right)}^2$

$\Delta k=275-\frac{800}{3}\text{erg.}$

$=\frac{25}{3}erg$

$=\frac{25}{3}\times {10}^{-7}J$

this energy forms to increase temp.

$\frac{25}{3}\times {10}^{-7}=3\times {10}^{-3}\times 4.2\times \Delta T$

$\Delta T=66\times {10}^{-3_0}C$

Answer: (B)