Question

The kinetic energy 'K' of particle moving in a straight line depends on the distance 'S' as K=a(S^2).the force acting on the particle will be
a. aS
b. 2maS
c. 2am
d. a(S^2)
Give reason.

Answer 1

It is normal in these equations to use 'a' to represent acceleration

However if this is the case then your equation must be wrong:

The dimensions of KE are Mass*Length^2/Time^2 (i.e. Nm, or Joules)
The dimensions of a(s^2 ) are Length^3/Time^2

Therefore the 2 cannot be equal.

I must therefore assume that a represents a constant

Using the above dimensions we have ML^2/T^2 = {a}L^2
(where {a} ar ethe dimensions of a)

So {a} = M/T^2

Now force has dimensions ML/T^2

So for the formula to be correct the force must be = L{a}

The only answer having these dimensions is .......?