Question

A 100 g of iron nail is hit by a \(1.5\) \(kg\) hammer striking at a velocity of \(60 \;ms^{–1}\). What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail?
[Specific heat capacity of iron = \(0.42\; Jg^{–1} °C^{–1}\)]

• A. 675°C
• B. 1600°C
• C. 16.07°C
• D. 6.75°C

Answer 1

The Correct Option is C

To determine the rise in the temperature of the iron nail, we need to calculate how much kinetic energy of the hammer is transferred to the nail as heat. Given that one-fourth of the hammer's energy is used to heat the nail, we can solve the problem as follows:

1. Calculate the Kinetic Energy (KE) of the hammer:

   The formula for kinetic energy is:

   KE = \frac{1}{2}mv^2

   where m is the mass of the hammer (1.5 kg) and v is the velocity (60 m/s):

   KE = \frac{1}{2} \times 1.5 \times (60)^2 = 2700 \; J

2. Calculate the energy transferred to the nail:

   Only one-fourth of the hammer's kinetic energy is used for heating the nail:

   E_{\text{nail}} = \frac{2700}{4} = 675 \; J

3. Calculate the rise in temperature of the nail:

   Using the formula for heat transfer, Q = mc\Delta T, where:

   • Q is the heat energy (675 J),
   • m is the mass of the nail (100 g),
   • c is the specific heat capacity of iron (0.42 \; Jg^{-1}°C^{-1}),
   • \Delta T is the rise in temperature.

   Substitute the known values into the formula:

   675 = 100 \times 0.42 \times \Delta T

   Solve for \Delta T:

   \Delta T = \frac{675}{100 \times 0.42} \approx 16.07 \; °C

The rise in temperature of the iron nail is approximately 16.07 \; °C. Therefore, the correct answer is:

Option: 16.07°C