UPSEE Solved Model Paper 7

The dimensions of tensile force (F), length (! ) and velocity (v) are
[F] = [MLT−2]
[l] = [L]
[v] = [LT−1]
Given:
v =

p

2l

(

F

m

)

1

2

⇒ m =

p2

4l2

×

F

v2

Now the dimension of m is
[m] =

[p]2

4[l]2

×

[F]

[v]2

p is a dimensionless quantity since it is only a number
⇒ [m] =

[MLT−2]

[L2][LT−1]2

⇒ [m] = [ML−3T0]
Hence, option 'D' is correct