JEE MAIN - Physics (2021 - 26th February Morning Shift - No. 24)
The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form y = $$-$$ 0.21 sin (x + 30t) is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is x $$\times$$ 10$$-$$2 N. Value of x is _________. (Round off to the nearest integer)
Answer
1215
Explanation
$$\mu = 0.135$$ gm/cm
$$\mu = 0.135 \times {{{{10}^{ - 3}}} \over {{{10}^{ - 2}}}}{{kg} \over m}$$
y = $$-$$0.21 sin (x + 30t)
$$v = {\omega \over K} = {{30} \over 1}$$ = 30 m/s
v = $$\sqrt {{T \over \mu }} $$
T = v2 $$\times$$ $$\mu$$
T = (30)2 $$\times$$ 0.135 $$\times$$ 10$$-$$1
T = 900 $$\times$$ 0.135 $$\times$$ 10$$-$$1
T = 12.15 N
T = 1215 $$\times$$ 10$$-$$2 N
x = 1215
$$\mu = 0.135 \times {{{{10}^{ - 3}}} \over {{{10}^{ - 2}}}}{{kg} \over m}$$
y = $$-$$0.21 sin (x + 30t)
$$v = {\omega \over K} = {{30} \over 1}$$ = 30 m/s
v = $$\sqrt {{T \over \mu }} $$
T = v2 $$\times$$ $$\mu$$
T = (30)2 $$\times$$ 0.135 $$\times$$ 10$$-$$1
T = 900 $$\times$$ 0.135 $$\times$$ 10$$-$$1
T = 12.15 N
T = 1215 $$\times$$ 10$$-$$2 N
x = 1215
Comments (0)
