JEE PYQ: Properties Of Matter Question 11
Question 11 - 2019 (08 Apr 2019 Shift 1)
A boy’s catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms$^{-1}$. Neglect the change in the area of cross-section of the cord while stretched. The Young’s modulus of rubber is closest to:
(1) $10^6$ N/m$^{-2}$
(2) $10^4$ N/m$^{-2}$
(3) $10^8$ N/m$^{-2}$
(4) $10^3$ N/m$^{-2}$
Show Answer
Answer: (1)
Solution
$\frac{1}{2}\left(\frac{YA}{L}\right)(\Delta l)^2 = \frac{1}{2}mv^2 \Rightarrow Y = \frac{mv^2 L}{A(\Delta l)^2} = \frac{0.02 \times 400 \times 0.42 \times 4}{\pi \times 36 \times 10^{-6} \times 0.04} \approx 2.3 \times 10^6$ N/m$^2$
BETA
