JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Heat & Thermodynamics

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}^{\circ} C^{- 1}

]

(A) $67 5^{\circ} C$
(B) $160 0^{\circ} C$
(C) $16.0 7^{\circ} C$ ✓ Correct
(D) $6.7 5^{\circ} C$

Answer: (C)

Solution

The moving hammer carries kinetic energy

\frac{1}{2} m v^{2} = \frac{1}{2} (1.5) (60)^{2} = 2700 J

, and only one fourth of this,

675 J

, is delivered to the nail as heat. The temperature rise then follows from

Q = m c Δ T

with the nail's mass

m = 100 g

and the specific heat

c = 0.42 J g^{- 1}^{\circ} C^{- 1}

kept in gram units to match, so

Δ T = \frac{675}{100 \times 0.42} = \frac{675}{42} \approx 16.07^{\circ} C

JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Heat & Thermodynamics →

JEE Main · 2022 · 24 Jun 2022 · Shift 2 · Heat & Thermodynamics

Solution

More JEE Main questions on Heat & Thermodynamics