Five forces `vec(F)_(1) ,vec(F)_(2) , vec(F)_(3) , vec(F)_(4)` , and `vec(F)_(5)` , are acting on a particle of mass `2.0kg` so that is moving with `4m//s^(2)` in east direction. If `vec(F)_(1)` force is removed, then the acceleration becomes `7m//s^(2)` in north, then the acceleration of the block if only `vec(F)_(1)` is action will be:

Options

A. `16m//s^(2)`
B. `sqrt(65)ms^(2)`
C. `sqrt(260)ms^(2)`
D. `sqrt(233)ms^(2)`

Answer

B

Explanation

`vec(F)_(1)+vec(F)_(2)+vec(F)_(3)+vec(F)_(4)+vec(F)_(5)=2(4hati)` .
and `vec(F)_(2)+vec(F)_(3)+vec(F)_(4)+vec(F)_(5)=2(7hatj)` .
From (i) and (ii), `vec(F)_(1)=8hati-14hatj` .
`vec(a)=vec(F)_(1)/(m)=4hati-7hatj` .
implies `a_(1)=sqrt(16+49)=sqrt(65)m//s^(2)` .