Write the dimensions of a × b in the relation E=(b-x2/a t), where E is the energy, x is the displacement, and t is the time.

Question

Write the dimensions of a × b in the relation E=(b-x2/a t), where E is the energy, x is the displacement, and t is the time. (A) M L2 T (B) M-1 L2 T1 (C) M L2 T-2 (D) M L T-2

Tardigrade Admin · Accepted Answer

Here, b and x2=L2 have same dimensions. Also, a=(L2/E × t)=(L2/(M L2 T-2) T)=M-1 T1 a × b=[M-1 L2 T1]

Q. Write the dimensions of $a \times b$ in the relation $E = \frac{b - x ^{2}}{a t}$ , where $E$ is the energy, $x$ is the displacement, and $t$ is the time.

$M L^{2} T$

$M^{- 1} L^{2} T^{1}$

$M L^{2} T^{- 2}$

$M L T^{- 2}$

Here, $b$ and $x^{2} = L^{2}$ have same dimensions.
Also, $a = \frac{L ^{2}}{E \times t} = \frac{L ^{2}}{( M L ^{2} T ^{- 2} ) T} = M^{- 1} T^{1}$
$a \times b = [M^{- 1} L^{2} T^{1}]$

Q. Write the dimensions of a×b in the relation E=atb−x2​, where E is the energy, x is the displacement, and t is the time.

ML2T

M−1L2T1

ML2T−2

MLT−2