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Question

(A) According to the principle of homogeneity of dimensions,the dimensions of each term in an equation must be the same.$1$. For the term $(t+c)$,the

Vedclass · Accepted Answer

$LT^{-2}, L, T$

Vedclass · Answer

(A) According to the principle of homogeneity of dimensions,the dimensions of each term in an equation must be the same.$1$. For the term $(t+c)$,the dimension of $c$ must be the same as the dimension of time $t$. Therefore,$[c] = [T]$.$2$. For the term $at$,the dimension of $at$ must be equal to the dimension of velocity $v$. Since $[v] = [LT^{-1}]$ and $[t] = [T]$,we have $[a][T] = [LT^{-1}]$,which gives $[a] = [LT^{-2}]$.$3$. For the term $\frac{b}{t+c}$,the dimension of this term must be equal to the dimension of velocity $v$. Since $[t+c] = [T]$ and $[v] = [LT^{-1}]$,we have $\frac{[b]}{[T]} = [LT^{-1}]$,which gives $[b] = [L]$.Thus,the dimensions are $[a] = [LT^{-2}]$,$[b] = [L]$,and $[c] = [T]$.

List-$I$	List-$II$
$(A)$ Angular momentum	$(I)$ $[ML^2T^{-1}]$
$(B)$ Torque	$(II)$ $[ML^2T^{-2}]$
$(C)$ Stress	$(III)$ $[ML^{-1}T^{-2}]$
$(D)$ Pressure gradient	$(IV)$ $[ML^{-2}T^{-2}]$

If the equation for the velocity of a particle at time $t$ is $v = at + \frac{b}{t+c}$,then the dimensions of $a, b, c$ are respectively:

Similar Questions

If $G$ is the gravitational constant and $u$ is the energy density,then which of the following quantities has the same dimensions as $\sqrt{uG}$?

Match List-$I$ with List-$II$.

List-$I$ List-$II$

$(A)$ Angular momentum $(I)$ $[ML^2T^{-1}]$

$(B)$ Torque $(II)$ $[ML^2T^{-2}]$

$(C)$ Stress $(III)$ $[ML^{-1}T^{-2}]$

$(D)$ Pressure gradient $(IV)$ $[ML^{-2}T^{-2}]$

Choose the correct answer from the options given below:

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The dimension of $\sqrt{\frac{\mu_0}{\varepsilon_0}}$ is the same as:

The dimensional formula $M L^{-1} T^{-2}$ does not represent which of the following physical quantities?

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