
If force (F), velocity (V) and time (T) are taken as fundamental units, the dimensions of mass are
A.
B.
C.
D.
Answer
500.1k+ views
10 likes
Hint: To solve this problem, use the formula for Newton’s second law of motion which gives relation between force, mass and acceleration. But acceleration can be written in terms of velocity and time. So, substitute this relation in the formula for force. Rearrange the equation and get the expression for mass of a body. Then write this obtained equation in dimensions form. This will be the dimensions of mass if force, velocity and time are taken as fundamental quantities.
Formula used:
Complete step by step answer:
According to Newton’s second law of motion, force is given by,
…(2)
Where, M is the mass of the body
A is the acceleration acting on the body
We know, acceleration is given by,
…(2)
Where, V is the velocity of the body
T is the times taken by the body
Substituting equation. (2) in equation. (1) we get,
Rearranging the above equation we get,
Hence, if force (F), velocity (V) and time (T) are taken as fundamental units, the dimensions of mass are .
So, the correct answer is “Option D”.
Note: There is an alternate method to solve this problem which takes much longer time to be solved as compared to the above solution.
According to the alternate method, take
Now, substitute the dimensions of force, velocity and time in it.
Equating the powers on the both the sides we get,
…(1)
…(2)
…(3)
Substituting equation. (1) in equation. (2) we get,
…(4}
Substituting equation. (1) and (4) in equation. (3) we get,
Hence, the dimensions of mass are .
Formula used:
Complete step by step answer:
According to Newton’s second law of motion, force is given by,
Where, M is the mass of the body
A is the acceleration acting on the body
We know, acceleration is given by,
Where, V is the velocity of the body
T is the times taken by the body
Substituting equation. (2) in equation. (1) we get,
Rearranging the above equation we get,
Hence, if force (F), velocity (V) and time (T) are taken as fundamental units, the dimensions of mass are
So, the correct answer is “Option D”.
Note: There is an alternate method to solve this problem which takes much longer time to be solved as compared to the above solution.
According to the alternate method, take
Now, substitute the dimensions of force, velocity and time in it.
Equating the powers on the both the sides we get,
Substituting equation. (1) in equation. (2) we get,
Substituting equation. (1) and (4) in equation. (3) we get,
Hence, the dimensions of mass are
Recently Updated Pages
Master Class 11 Business Studies: Engaging Questions & Answers for Success

Master Class 11 Economics: Engaging Questions & Answers for Success

Master Class 11 Accountancy: Engaging Questions & Answers for Success

Master Class 11 Computer Science: Engaging Questions & Answers for Success

Master Class 11 Maths: Engaging Questions & Answers for Success

Master Class 11 English: Engaging Questions & Answers for Success

Trending doubts
The flightless birds Rhea Kiwi and Emu respectively class 11 biology CBSE

1 Quintal is equal to a 110 kg b 10 kg c 100kg d 1000 class 11 physics CBSE

Name the Largest and the Smallest Cell in the Human Body ?

Whales are warmblooded animals which live in cold seas class 11 biology CBSE

Where can free central placentation be seen class 11 biology CBSE

What is the chemical name of Iron class 11 chemistry CBSE
