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 4 times its original value. (B) The unit of acceleration becomes 8 times its original value. (C) The unit of momentum becomes 4 times its original value. (

Step-by-step solution

Let the original units of mass, length, and time be M , L , and T . The new units are M' = M , L' = 2L , and T' = T/2 . Evaluating each statement using dimensional formulas: (A) Velocity [LT⁻¹] : The new unit is L'(T')⁻¹ = (2L)(T/2)⁻¹ = 4[LT⁻¹] . Statement (A) is correct. (B) Acceleration [LT⁻²] : The new unit is L'(T')⁻² = (2L)(T/2)⁻² = 8[LT⁻²] . Statement (B) is correct. (C) Momentum [MLT⁻¹] : The new unit is M'L'(T')⁻¹ = M(2L)(T/2)⁻¹ = 4[MLT⁻¹] . Statement (C) is correct. (D) Force [MLT⁻²] : The new unit is M'L'