When a body is in SHM, then match the following .
`{:(" List - I "," List- II"),(A."Vlecity is maximum",I. " At extreme position"),(B."KEis"((3)/(4))^(th)"oh the total energy",II." At mean position"),(C."PE is "((3)/(4))^(th)"of total energy",III. " At half of the amplitude"),(D."Acceleration is maximum",IV. ""At (sqrt(3))/(2)"times of the amplitude"):}`

Options

A. `{:(A,B,C,D),(III,I,IV,II):}`
B. `{:(A,B,C,D),(I,III,IV,II):}`
C. `{:(A,B,C,D),(II,III,IV,I):}`
D. `{:(A,B,C,D),(II,I,IV,III):}`

Answer

C

Explanation

(A) At mean position, velocity is mas ` = Aomega`
(B) In SHM , total Energy ` = (1)/(2) KA^(2) " ". . . (i)`
and `KE = (1)/(2) K(A^(2)-x^(2))" ". . . (ii)`
`:. KE = (3)/(4)TE`
From Eqs. (i) and (ii), we get
`(1)/(2)kA^(2)-(1)/(2)kx^(2)=(3)/(4)TE=(3)/(4)((1)/(2)KA^(2))`
`rArr 4A^(2) - 4x^(2) = 3A^(2)`
`rArr A^(2) = 2x^(2) rArr x = pm (A)/(2)`
(C) `PE= (1)/(2) kx^(2) and TE = (1)/(2) kA^(2)`
`:. PE = (3)/(4) TE rArr (1)/(2) kx^(2) = (3)/(4) ((1)/(2)kA^(2))`
`rArr x^(2) = (3)/(4)A^(2) rArr x = pm (sqrt(3))/(2)A`
(D) At extreme position, acceleration is maximum.
Hence, `(A) to II, (B) to III, (C) to IV, (D) to I`