Question

If force (F), momentum (P) and mass(M) are fundamental quantities in the System of units, then dimension formula for length (L) and time (T) will be​

Answer 1

Explanation:

Length -> [M^0 L^1 T^0]

Time -> [M^0 L^0 T^0]

Answer 2

Answer :-

To solve this question, we have to find the formulas of length and time with respect to force, momentum and mass.

Calculating dimensional formula for Time :-

➩ F = Change in momentum/Time

➩ F = P/T

➩ T = P/F

➩ T = P F⁻¹

where

• T is time
• P is momentum
• F is force

Calculating dimensional formula for length :-

➩ Force = Mass × Acceleration

➩ Force = M × (v - u)/t

➩ F = M × S t⁻²

➩ F = M × S × (P F⁻¹) ⁻²

➩ F = M × S × P⁻² F²

➩ S = F / M × P⁻² × F²

➩ S = M⁻¹ P² F⁻¹

where

• S is distance travelled
• M is Mass
• P is momentum
• F is force