Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NEET
Exam
NEET
Subject
Physics
Chapter
Units and Dimensions

NEET · Physics · Units and Dimensions

Consider a system of units where the standard unit of length is...

Consider a system of units where the standard unit of length is doubled and the standard unit of time is halved, while the unit of mass remains unchanged. Read the following statements regarding the new units of derived quantities:

(A) The unit of velocity becomes 44 times its original value.
(B) The unit of acceleration becomes 88 times its original value.
(C) The unit of momentum becomes 44 times its original value.
(D) The unit of force becomes 44 times its original value.

How many of the above statements are correct?

Options

  1. AOnly one
  2. BOnly two
  3. CAll four
  4. DOnly three

Correct answer

D. Only three

Step-by-step solution

Let the original units of mass, length, and time be MM, LL, and TT.
The new units are M′=MM' = M, L′=2LL' = 2L, and T′=T/2T' = T/2.

Evaluating each statement using dimensional formulas:

(A) Velocity [LT−1][LT^{-1}]: The new unit is L′(T′)−1=(2L)(T/2)−1=4[LT−1]L'(T')^{-1} = (2L)(T/2)^{-1} = 4[LT^{-1}]. Statement (A) is correct.

(B) Acceleration [LT−2][LT^{-2}]: The new unit is L′(T′)−2=(2L)(T/2)−2=8[LT−2]L'(T')^{-2} = (2L)(T/2)^{-2} = 8[LT^{-2}]. Statement (B) is correct.

(C) Momentum [MLT−1][MLT^{-1}]: The new unit is M′L′(T′)−1=M(2L)(T/2)−1=4[MLT−1]M'L'(T')^{-1} = M(2L)(T/2)^{-1} = 4[MLT^{-1}]. Statement (C) is correct.

(D) Force [MLT−2][MLT^{-2}]: The new unit is M′L′(T′)−2=M(2L)(T/2)−2=8[MLT−2]M'L'(T')^{-2} = M(2L)(T/2)^{-2} = 8[MLT^{-2}]. Statement (D) is incorrect (it becomes 88 times, not 44 times).

Therefore, exactly three statements are correct.

Answer: Only three
Practice Units and Dimensions on Quantrex Academy →

More from Units and Dimensions

If the errors involved in the measurement of a side and the mass of a cube are 2\% and… MHT CET Medical 2026If the mass of the object is measured as m = (7 ∓ 0.14) kg and the density is measured as… MHT CET Medical 2026Consider that σ_s , k_B , b represent Stefan-Boltzmann constant, Boltzmann constant and… NEET 2026The speed of light in vacuum is taken as unity. If light takes 6 min 40 s to reach the… NEET 2026Each side of a metallic cube of mass 5.580 kg is measured to be 9.0 cm. Keeping the… NEET 2026A physical quantity P is related to four observations a, b, c and d as follows : P=a^3… NEET 2025A balloon is made of a material of surface tension S and its inflation outlet (from where… NEET 2025The quantities which have the same dimensions as those of solid angle are: NEET 2024 Full Units and Dimensions list All NEET PYQs