Answer:
LHS=RHS=[L]
Explanation:
Given mathematical expression:

where: dimension:
s = displacement length ![[L]](https://tex.z-dn.net/?f=%5BL%5D)
u = initial velocity ![[L.T^{-1}]](https://tex.z-dn.net/?f=%5BL.T%5E%7B-1%7D%5D)
t = time ![[T]](https://tex.z-dn.net/?f=%5BT%5D)
a = acceleration ![[L.T^{-2}]](https://tex.z-dn.net/?f=%5BL.T%5E%7B-2%7D%5D)
now using dimensional analysis:
![[L]=[L.T^{-1}]\times [T]+[L.T^{-2}] [T]^2](https://tex.z-dn.net/?f=%5BL%5D%3D%5BL.T%5E%7B-1%7D%5D%5Ctimes%20%5BT%5D%2B%5BL.T%5E%7B-2%7D%5D%20%5BT%5D%5E2)
we know that the ratio and constants have no dimension.
![[L]=[L]+[L]](https://tex.z-dn.net/?f=%5BL%5D%3D%5BL%5D%2B%5BL%5D)
as we know that only similar dimensions can be added or subtracted therefore we get a correct conclusion.
<em>However we can deduce the operators between the equations and can neither check for the validity of the constants. We can only check for the dimension of the terms involved.</em>
The book is lifted upward, but gravity points down, so the work done by gravity must be negative (so you can eliminate options 1 and 3).
The force exerted on the book by gravity has magnitude
<em>F</em> = <em>mg</em> = (10 N) (9.80 m/s^2) = 9.8 N ≈ 10 N
You raise the book 1.0 m in the opposite direction, so the work done is
<em>W</em> = (10 N) (-1.0 m) = -10 J