A uniform circular disc of mass 2 m and radius R placed freely on a horizontal smooth surface as shown in the figure- 5.116.A particle of mass m is connected to the circumference of the disc with a massless string. Now an impulse J is applied on the particle in the directions shown by dotted line. The acceleration of centre of mass of the disc just after application of implues is `("If J "= 10 N -sec ., m=sqrt10 kg and R= 25cm )`

Options

A. `1 m//s^(2)`
B. `2m//s^(2)`
C. `3 m//s^(2)`
D. `4m//s^(2)`

Explanation

`T=2ma_(c )` …(i)
`RT_(1)=(2mR^(2))/(2)alpha` …(ii)
`T+m(a_(c )+alpha R)=(mJ^(2))/(m^(2)2R)`
`T+(T)/(2)+T=(J^(2))/(2mR)`
`therefore (5T)/(2)=(J^(2))/(2mR)`
`T=(J^(2))/(5mR)`
`a_(c )=(T)/(2m)=(J^(2))/(5mR2m)=(J^(2))/(10m^(2)R)`
putting all the values `a_(c )=4 m//s^(2)`