wiz-icon
MyQuestionIcon
MyQuestionIcon
4
You visited us 4 times! Enjoying our articles? Unlock Full Access!
Question

The equation for a wave travelling in x direction on a string is given as
y=10sin(πt0.5x), where y and x are in m and time(t) in sec. Find the acceleration of a particle at x=π m at time t=1 sec.

A
10π m/s2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
10π2 m/s2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
5π m/s2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
5π m/s2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 10π2 m/s2
We know,
Velocity of particle vP=yt=10πcos(πt0.5x)
Similarly, acceleration of particle can be obtained by partial differentiation of velocity w.r.t time (keeping x constant).
aP=vPt
aP=π×10πsin(πt0.5x)
aP=10π2sin(πt0.5x)
substituting x=π m & t=1 sec in above equation we get,
aP=10π2sin(π0.5π)
aP=10π2sinπ2
aP=10π2 m/s2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon