JEE MAIN - Physics (2020 - 8th January Evening Slot - No. 12)
A transverse wave travels on a taut steel wire
with a velocity of v when tension in it is
2.06 × 104 N. When the tension is changed to
T, the velocity changed to v/2. The value of T
is close to :
30.5 × 104 N
2.50 × 104 N
10.2 × 102 N
5.15 × 103 N
Explanation
$$v = \sqrt {{T \over \mu }} $$
$$ \therefore $$ $${{{v_1}} \over {{v_2}}} = \sqrt {{{{T_1}} \over {{T_2}}}} $$
v1 = v, v2 = $${v \over 2}$$
$$ \Rightarrow $$ $${v \over {{v \over 2}}} = $$ $$\sqrt {{{2.06 \times {{10}^4}} \over {{T_2}}}} $$
$$ \Rightarrow $$ T2 = $${{{2.06 \times {{10}^4}} \over 4}}$$ = 5.15 × 103 N
$$ \therefore $$ $${{{v_1}} \over {{v_2}}} = \sqrt {{{{T_1}} \over {{T_2}}}} $$
v1 = v, v2 = $${v \over 2}$$
$$ \Rightarrow $$ $${v \over {{v \over 2}}} = $$ $$\sqrt {{{2.06 \times {{10}^4}} \over {{T_2}}}} $$
$$ \Rightarrow $$ T2 = $${{{2.06 \times {{10}^4}} \over 4}}$$ = 5.15 × 103 N
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