Question

If string of length 10 m and mass 10 gm is connected with two
blocks as in figure then speed of transverse wave in string will
be:
A. √2*10/3 m/s
B. √10^5/3 m/s
C. √200/3 m/s
D. √100/3 m/s​

Answer 1

Given : If string of length 10 m and mass 10 gm is connected with two blocks as in figure.

To find : The speed of transverse wave in string.

solution : from block of mass 5kg,

T - 5kg × 10m/s² = 5kg × a

⇒T - 50 = 5a ......(1)

from block of mass 10kg,

10kg × 10m/s² - T = 10kg × a

⇒100 - T = 10a .......(2)

from equations (1) and (2) we get,

50 = 15a ⇒a = 10/3

so, T - 50 = 5 × 10/3 ⇒T = 200/3 N

using formula, v = √{T/μ}

here T = 200/3 N, μ = m/l = (10 × 10¯³ kg)/(10m) = 10¯³ kg/m

so v = √{200/3/10¯³} = 100 √(20/3) m/s

Therefore the speed of transverse wave in string is 100√(20/3) m/s