You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Velocity Displacement Relationship

A particle de...

Question

A particle describes linear S.H.M. Its velocities are $3 m s^{- 1}$ and $2 m s^{- 1}$ when its displacements are 2 m and 3 m respectively from mean position. Find length of the path?

1.2 m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4.6 m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6.7 m

No worries! We‘ve got your back. Try BYJU‘S free classes today!

7.2 m

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D 7.2 m
$v = ω \sqrt{A^{2} - x^{2}}; \frac{3}{2} = \frac{\sqrt{A^{2} - 4}}{\sqrt{A^{2} - 9}}$
Squaring, $\frac{9}{4} = \frac{(A^{2} - 4)}{(A^{2} - 9)}$
$9 A^{2} - 81 = 4 A^{2} - 16; 5 A^{2} = 65$
$A^{2} = \frac{65}{5} = 13; A = \sqrt{13} m$
$∴$ Length of the path $= 2 A = 2 \sqrt{13} = 7.2 m .$

Suggest Corrections

Similar questions

Q. A particle describes linear S.H.M. Its velocities are

3 m s^{- 1}

and

2 m s^{- 1}

when its displacements are 2 m and 3 m respectively from mean position. Find length of the path?

A particle is moving in a straight line with SHM. Its velocity has the values $3 m / s$ and $2 m / s$ when its distances from mean position are $1 m$ and $2 m$ respectively. Find the length of its path and period of its motion.

Q. A body executing

S . H . M .

along a straight line has a velocity of

3 m s^{- 1}

when it is at a distance of

4 m

from its mean position and

4 m s^{- 1}

when it is at a distance of

3 m

from its mean position. Its angular frequency and amplitude are:

Q. A particle is describing simple harmonic motion. If its velocities are

v_{1}

and

v_{2}

when the displacements from the mean position are

y_{1}

and

y_{2}

respectively, then its time period is

Q. A particle executes SHM has amplitude of 4m and its acceleration at a distance of 1m from mean position is

3 {m / s}^{2}

. What will be its velocity when it is at a distance of 2m from its mean position

Join BYJU'S Learning Program

A particle describes linear S.H.M. Its velocities are 3ms−1 and 2ms−1 when its displacements are 2 m and 3 m respectively from mean position. Find length of the path?

The correct option is D 7.2 mv=ω√A2−x2;32=√A2−4√A2−9 Squaring, 94=(A2−4)(A2−9) 9A2−81=4A2−16;5A2=65 A2=655=13;A=√13m ∴ Length of the path =2A=2√13=7.2m.

A particle describes linear S.H.M. Its velocities are $3 m s^{- 1}$ and $2 m s^{- 1}$ when its displacements are 2 m and 3 m respectively from mean position. Find length of the path?