Question

195. The velocity of particle is related to time according to equation
V = ct 3. The dimensions of constant C are ____.
A. L-1 T-1
B. LT-3
c. LT-4
D. L-2 T-2​

Answer 1

Your Question:

The velocity of particle is related to time according to equationV = ct^3. The dimensions of constant C are ____.

Answer : (c) LT^(-4)

Explanation

Dimension of Velocity =

$[M^{0} LT^{ - 1} ]$

According to Principle of Homogeneity,

Dimensions in RHS should be equal to Dimensions in the LHS.

Here, 'c' is multiplied by [T]^3

Let dimensions of C be =

$[M^{x} L^{y} T^{ z} ]$

=>

$[M^{0} LT^{ - 1} ] = [M^{x} L^{y} T^{ z} ] \times [ M^{0} L^{0} T^{ 3} ] \\ \\ = > \frac{[M^{0} LT^{ - 1} ]}{ [M^{x} L^{y} T^{ z} ] } = [ M^{0} L^{0} T^{ 3} ]$

From above Equation, we get

$0 - x = 0 \: \: ....(i) \\ 1 - y = 0 \: ....(ii) \\ - 1 - z = 3 \: ....(iii)$

Therefore,

$x = 0 \\ y = 1 \\ z = 4$

Hemce Dimension of C =

$[M^{0} L^{1} T^{ 4} ] \\ \\ = [ L T^{ 4} ]$

Hope this helps :))

Answer 2

C option is right
Hope it helps you