Three forces `vec(F_(1))=23hat(j)+3hat(j)-hat(k), vec(F_(2))=4hat(i)-hat(j)-2hat(k)` and `vec(F_(3))=23hat(j)+3hat(k)N`act on a block of mass `5kg`. Calculate the acceleration of the particle.

Options

A. 10
B. 5
C. 15
D. 1.5

Answer

B

Explanation

Net force
`vec(F)=vec(F_(1))+vec(F_(2))=vec(F_(3))`
`=(3hat(i)+2hat(j)-hat(k))+(4hat(i)-hat(j)-2hat(k))+(23hat(i)+3hat(k))`
`=7hat(i)+24hat(j)`
`|vec(F)|=F=sqrt((7)^(2)+(24)^2)=25N`
Acceleration of the block
`a=(F)/(m)=(25)/(5)=5m//s^(2)`