Question 165: Properties of Matter

Question

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 0.02kg 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:

Accepted Answer

When rubber cord is stretched, then it stores potential energy and when released, this potential energy is given to the stone as kinetic energy.
So, potential energy of stretched cord = kinetic energy of stone
$$ \Rightarrow {1 \over 2}Y{\left( {{{\Delta L} \over L}} ight)^2}A\,.\,L = {1 \over 2}m{v^2}$$
Here, $$\Delta$$L = 20 cm = 0.2 m, L = 42 cm = 0.42 m, v = 20 ms
$$-$$1
, m = 0.02 kg, d = 6 mm = 6 $$	imes$$ 10
$$-$$3
m
$$	herefore$$ $$A = \pi {r^2} = \pi {\left( {{d \over 2}} ight)^2} = \pi {\left( {{{6 	imes {{10}^{ - 3}}} \over 2}} ight)^2}$$
$$ = \pi {(3 	imes {10^{ - 3}})^2} = 9\pi  	imes {10^{ - 6}}{m^2}$$
On substituting values, we get
$$Y = {{m{v^2}L} \over {A{{(\Delta L)}^2}}} = {{0.02 	imes {{(20)}^2} 	imes 0.42} \over {9\pi  	imes {{10}^{ - 6}} 	imes {{(0.2)}^2}}}$$
$$ \approx 3.0 	imes {10^6}N{m^{ - 2}}$$
So, the closest value of Young's modulus is 10
6
Nm
$$-$$2
.

Answer

104 Nm–2

Answer

106 Nm–2

Answer

108 Nm–2

Answer

103 Nm–2

Properties of Matter

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