In two different systems of units, acceleration is represented by the same number while a velocity is represented by numbers in the ratio 1: 3. The ratios of unit of length and time are, respectively,

Question

In two different systems of units, acceleration is represented by the same number while a velocity is represented by numbers in the ratio 1: 3. The ratios of unit of length and time are, respectively, (A) (1/3), (1/9) (B) (1/9), (1/3) (C) 3, 9 (D) 9, 3

Tardigrade Admin · Accepted Answer

Length, l=(v2/a); time, t=(v/a) ⇒ Ratio of unit of length =((1/3))2=(1/9) ⇒ Ratio of unit of time =(1/3)

Q. In two different systems of units, acceleration is represented by the same number while a velocity is represented by numbers in the ratio $1 : 3$ . The ratios of unit of length and time are, respectively,

$\frac{1}{3}$ , $\frac{1}{9}$

$\frac{1}{9}$ , $\frac{1}{3}$

$3, 9$

$9, 3$

Length, $l = \frac{v ^{2}}{a};$ time, $t = \frac{v}{a}$
$\Rightarrow$ Ratio of unit of length $= (\frac{1}{3})^{2} = \frac{1}{9}$
$\Rightarrow$ Ratio of unit of time $= \frac{1}{3}$

Q. In two different systems of units, acceleration is represented by the same number while a velocity is represented by numbers in the ratio 1:3. The ratios of unit of length and time are, respectively,

31​, 91​

91​, 31​

3,9

9,3