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 = \(0.42\; Jg^{–1} °C^{–1}\)]
[Specific heat capacity of iron = \(0.42\; Jg^{–1} °C^{–1}\)]
- 675°C
- 1600°C
- 16.07°C
- 6.75°C
The Correct Option is C
Solution and Explanation
\(\frac{1}{2} \times 1.5 \times 60^2 \times \frac{1}{4} = 100 \times 0.42 \times \triangle \;T\)
\(\triangle\; T = \frac{1.5\times 60^2}{8\times 100 \times 0.42} = 16.07 \;\degree C\)
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Concepts Used:
Work-Energy Theorem
The work and kinetic energy principle (also known as the work-energy theorem) asserts that the work done by all forces acting on a particle equals the change in the particle's kinetic energy. By defining the work of the torque and rotational kinetic energy, this definition can be extended to rigid bodies.
The change in kinetic energy KE is equal to the work W done by the net force on a particle is given by,
W = ΔKE = ½ mv2f − ½ mv2i
Where,
vi → Speeds of the particle before the application of force
vf → Speeds of the particle after the application of force
m → Particle’s mass
Note: Energy and Momentum are related by, E = p2 / 2m.