Home
Class 11
PHYSICS
A new system of units is proposed in wh...

A new system of units is proposed in which unit of mass is `alpha kg,` unit of length `beta` m and unit of time `lambda s.` How much will 5 J measure in this new system ?

A

`5alphabeta^(2)gamma^(-2)`

B

`5alpha^(-1)beta^(-2)gamma^(2)`

C

`5alpha^(-2)beta^(-1)gamma^(-2)`

D

`5alpha^(-1)beta^(2)gamma^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Joule's is a unit of energy.
`{:(SI,"New system"),(n_(1)=5,n_(2)=?),(M_(1)=1kg,M_(2)=alphakg),(L_(1)=1m,L_(2)=betam),(T_(1)=1s,T_(2)=gammas):}`
dimensional formula of energy is `[ML^(2)T^(-2)]`. Comparing with `[M^(a)L^(b)T^(c)],` we get
`a=1,b=2,c=-2`
As `n_(2)=n_(1)((M_(1))/(M_(2)))^(a)((L_(1))/(L_(2)))^(b)((T_(1))/(T_(2)))^(c)`
`=5((1kg)/(alphakg))^(1)((1m)/(betam))^(2)((1s)/(gammas))^(-2)=(5gamma^(2))/(alphabeta^(2))=5alpha^(-1)beta^(-2)gamma^(2)`
Promotional Banner

Topper's Solved these Questions

  • UNITS AND MEASUREMENTS

    NCERT FINGERTIPS|Exercise Higher Order Thinking Skills|10 Videos

  • UNITS AND MEASUREMENTS

    NCERT FINGERTIPS|Exercise NCERT Exemplar|12 Videos

  • UNITS AND MEASUREMENTS

    NCERT FINGERTIPS|Exercise Dimensional Formulae And Dimensional Equations|8 Videos

  • THERMODYNAMICS

    NCERT FINGERTIPS|Exercise Assertion And Reason|15 Videos

  • WAVES

    NCERT FINGERTIPS|Exercise Assertion And Reason|15 Videos

Similar Questions

Explore conceptually related problems

If in a system unit of mass is 5kg, unit of length is 10m and unit of time as 5sec, then what will be the value of 1 unit energy in new system.

In a new system of units, unit of mass is taken as 50 kg. unit of length as 100 m and unit of time is 1 minute. What will be the weight of a body in this system, if in SI sysem, its weight is 10 N?

A calorie is a unit of heat or energy and it equals about 4.2 J, where 1 J = 1 kg m^(2) s^(-2) . Suppose we employ a system of units in which the unit of mass equals alpha kg , the unit of length equals is beta m , the unit of time is gamma s . Show tthat a calorie has a magnitude 4.2 alpha^(-1) beta^(-1) gamma^(2) in terms of the new units.

If the unit of force is 1 kN, unit of length 1 km and unit of time is 100s, what will be the unit of mass?

Suppose two students are trying to make a new measurement system so that they can use it like a code measurement system and others do not understands it. Instead of taking 1kg, 1m and 1 sec, as basic unit they took unit of mass as alpha kg , the unit of length as beta m and unit of times as gamma second. They called power in new system as ACME then match the two columns. {:(,"Column-I",,"Column-II"),((a),"1N in new system",(p),alpha^(-1) beta^(-2) gamma^(2)),((b),"1J in new system",(q),alpha^(-1) beta^(-1) gamma^(2)),((c),"1 pascal (SI unit of pressure) in new system",(r),alpha^(-1)beta gamma^(2)),((d),alpha "ACME in watt",(s),alpha^(2) beta^(2) gamma^(-3)):}

Suppose two students trying to make a new measurement system so that they can use it like a code measurement system and others do not understand it Instead of taking 1 kg, 1 m and 1 second, as basic unit they took unit of mass as alpha kg, the unit of length as beta m and unit of times as gamma second. They called power in new system as "Aakash", then find The value of alpha "Aakash" in watt.

Suppose two students are trying to make a new measurement system so that they can use it like a code measurement. Instead of taking 1 kg, 1 m 1 s, as the basic unit they took unit of mass as alpha kg, the unit of length as beta m and the unit of tme as gamma s. They called the new system as ACME. Column I represents the units of the physical quantities, Column II represents the ACME units and Column III represents the CGS units of the physical quantities. Which of the following represents the correct combination for a physical quantity known as rate of energy?

If the unit of force is 100 N, unit of length is 10m and unit of time is 100 s, what is the unit of mass in this system of units ?