Question

1 : The velocity 'v' of a particle depends upon the time t according to the equation
$v = a + bt + \frac{c}{d + t}$
write the dimensions of a,b,c and d.

​( please can any one do this )

Answer 1

Answer:

From the principal of homogeneity,

[a]=[v]or[a]=[LT

−1

]

[bt]=[v]or[b]=

[t]

[v]

=

[T]

[LT

−1

]

or, [b]=[LT

−2

]

Similarly, [d]=[t]=[T]

Further,

[d+t]

[c]

=[v]or[c]=[v][d+t]

or, [c]=[LT

−1

][T]or[c]=[L]