A solid cylinder of mg 50 kg and radius 0.5 m is free to rotate about the horizontal axis. A massless string is wound round the cylinder with one end attached to and hanging freely. Tension in the string required to produce angular acceleration of revolutions $s ^ { - 2 }$ is
The vibration of a string of length 60 cm fixed at both ends are represented by $ y=4sin (\frac { \pi x}{15}) cos (96 \pi t) $ where x and y are in cm and t in second. the particle velocity at x=7.5 cm and t=0.25 s is
A $100$ Hz sinusoidal wave is travelling in the positive x-direction along a string with a linear mass density of $3.5 \times 10^{-3}$ kg/m and a tension of $35$ N. At time t = 0, the point x = 0 has zero displacements and the slope of the string is $\pi/20$. Then select the wrong alternative
A uniform string fixed at both ends is vibrating in 3rd harmonic and equation $y = 4 ( \mathrm { cm } )$ $\sin \left[ \left( 0.8 \mathrm { cm } ^ { - 1 } \right) \times \right] \cos \left[ \left( 400 \pi \mathrm { s } ^ { - 1 } \right) t \right]$The length of the vibrating string is
The wave function for the wave pulse is $ Y (X,t) = \frac {0.1a^3}{a^2 +(X-Vt)^2} with a = 4 cm. At X = 0 $ The displacement y (x,t) is observed to decreases from its maximum value to half of that value in time $ t = 2 \times 10^{-3} s $ choose the correct statement
A string is properly tuned:
A heavy flexible rope hangs vertically. The speed of a transverse wave at a height $h$ from the free end is
Small amplitude progressive waves in a stretched string have a speed of 100 cm/s and frequency 100 Hz. The phase difference between two points 2.75 cm apart on the string, in radians is
A tension in wire is 40N and 10 m of wire has a mass of 0.01 kg . The speed of transverse waves in m/s in the wire is :
A string of mass $2.5\ kg$ is under a tension of $200\ N$. The length of the stretched string is $20.0\ m$. If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in