In a new system, the unit of mass is made 10 times, the unit of length is made 1/100 times and unit of time is made 10 times. Magnitude of 1J in the new system of unit is 10^x. What is the value of x  

Asked by Anil | 21st May, 2017, 09:49: PM

Expert Answer:

begin mathsize 12px style The space dimensions space of space joule space in space the space regular space system space of space units space is
left square bracket straight J right square bracket equals left square bracket ML squared straight T to the power of negative 2 end exponent right square bracket
In space the space new space system comma space straight M rightwards arrow 10 straight M semicolon space straight L rightwards arrow straight L over 100 semicolon straight T rightwards arrow 10 straight T
therefore open square brackets 1 straight J close square brackets subscript new equals open square brackets 10 straight M close square brackets cross times open square brackets straight L over 100 close square brackets squared cross times open square brackets 10 straight T close square brackets to the power of negative 2 end exponent
therefore open square brackets 1 straight J close square brackets subscript new equals open square brackets ML squared straight T to the power of negative 2 end exponent close square brackets cross times open parentheses 10 cross times fraction numerator 1 over denominator 100 cross times 100 end fraction cross times fraction numerator 1 over denominator 10 cross times 10 end fraction close parentheses
therefore open square brackets 1 straight J close square brackets subscript new equals 10 to the power of negative 5 end exponent open square brackets ML squared straight T to the power of negative 2 end exponent close square brackets
therefore straight x equals negative 5 end style

Answered by Romal Bhansali | 22nd May, 2017, 12:43: PM