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ICSE Class 10 Physics Question 3 of 25

Model Paper 1 — Question 12

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12
Question

Question 1(xii)

Two blocks P and Q of different metals having their masses in the ratio 3 : 2 are given the same amount of heat. Their temperature rise by the same amount. The ratio of their specific heat capacities is :

  1. √3 : √2
  2. 9 : 4
  3. 2 : 3
  4. 3 : 2
Answer

2 : 3

Reason — Let masses of P and Q be mP\text{m}_\text{P} and mQ\text{m}_\text{Q} and their specific heat capacities cP\text{c}_\text{P} and cP\text{c}_\text{P} respectively. Let heat given be Q and temperature change is ΔT.

Given,

MPMQ=32\dfrac{\text{M}_\text{P}}{\text{M}_\text{Q}}=\dfrac{3}{2}

As, Q = McΔT\text{Q = McΔT}

According to question,

MPcPΔT=MQcQΔT\text{M}_\text{P}\text{c}_\text{P}Δ\text T=\text{M}_\text{Q}\text{c}_\text{Q}Δ\text T

MPcP=MQcQ\text{M}_\text{P}\text{c}_\text{P}=\text{M}_\text{Q}\text{c}_\text{Q}

cPcQ=MQMP=23\dfrac{\text{c}_\text{P}}{\text{c}_\text{Q}} = \dfrac{\text{M}_\text{Q}}{\text{M}_\text{P}}=\dfrac{2}{3}