If the present units of length,time,and mass | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the original units be $L_1 = 1 \; m$,$T_1 = 1 \; s$,$M_1 = 1 \; kg$. The new units are $L_2 = 100 \; m$,$T_2 = 100 \; s$,$M_2 = 0.1 \; kg$.$1$

Vedclass · Accepted Answer

The new unit of force is decreased $\frac{1}{1000}$ times

Vedclass · Answer

(B) Let the original units be $L_1 = 1 \; m$,$T_1 = 1 \; s$,$M_1 = 1 \; kg$. The new units are $L_2 = 100 \; m$,$T_2 = 100 \; s$,$M_2 = 0.1 \; kg$.$1$. Velocity $(v = L T^{-1})$: New unit $v_2 = L_2 T_2^{-1} = 100 \; m / 100 \; s = 1 \; m/s$. Thus,velocity remains the same.$2$. Force $(F = M L T^{-2})$: New unit $F_2 = M_2 L_2 T_2^{-2} = (0.1 \; kg) 	imes (100 \; m) / (100 \; s)^2 = 0.1 	imes 100 / 10000 = 0.001 \; N = \frac{1}{1000} \; N$. The new unit of force is $\frac{1}{1000}$ times the original.$3$. Energy $(E = M L^2 T^{-2})$: New unit $E_2 = M_2 L_2^2 T_2^{-2} = (0.1 \; kg) 	imes (100 \; m)^2 / (100 \; s)^2 = 0.1 	imes 10000 / 10000 = 0.1 \; J = \frac{1}{10} \; J$.$4$. Pressure $(P = M L^{-1} T^{-2})$: New unit $P_2 = M_2 L_2^{-1} T_2^{-2} = (0.1 \; kg) / (100 \; m 	imes (100 \; s)^2) = 0.1 / (100 	imes 10000) = 0.1 / 10^6 = 10^{-7} \; Pa$.

If the present units of length,time,and mass $(m, s, kg)$ are changed to $100 \; m, 100 \; s, 0.1 \; kg$,then:

Similar Questions

In a nuclear power plant,the energy released depends on the mass of the uranium sample $(m)$,the length of the oscillator $(\ell)$,and the frequency $(f)$ of oscillation as $E = m^{x} \ell^{y} f^{z}$. Then,what is the value of $x + y + z$?

If velocity of light $c$,Planck's constant $h$,and gravitational constant $G$ are taken as fundamental quantities,then express length in terms of dimensions of these quantities.

The formula is $X = 5YZ^2$,where $X$ and $Z$ have dimensions of capacitance and magnetic field,respectively. What are the dimensions of $Y$ in $SI$ units?

$A$ physical quantity of the dimensions of length that can be formed out of $c, G$ and $\frac{e^2}{4\pi \varepsilon_0}$ is $[c$ is velocity of light,$G$ is the universal gravitational constant and $e$ is charge$]$.

The velocity of a particle depends upon the time $t$ according to the equation $v = \sqrt{ab} + bt + \frac{c}{d + t}$. The physical quantities which are represented by $a, b, c$ and $d$,are in the following order:

Vedclass Test Series

Exam Paper Generator

Online Exam Module