Which of the following pair of quantities have the same dimensional formula? *
(a) Frequency, Time
(b) Force, linear momentum
(c) Work, energy
(d) Acceleration, velocity
Answers
Answer:
a) frequency dimensional formula is [T^-1]
time dimensional formula is [T]
b) Force dimensional formula is [MLT^-2]
Linear momentum dimensional formula is [MLT^-1].
c) Work dimensional formula is [ML^2T^_2].
Energy dimensional formula is [ML^2T^-2].
d) acceleration dimensional formula is [LT^-2].
velocity dimensional formula is [LT^-1].
SO THE OPTION IS 'C'.
HOPE THIS HELPS !
Quantity with same dimensional formula is :
c) work, energy
In option a), frequency is inverse of time.
Hence, frequency has dimensional formula - [T-¹] while time has dimensional formula - [T]
In option b), force has formula - mass*acceleration due to gravity, while linear momentum is calculated by - mass*velocity.
Hence, force has dimensional formula - [MLT-²] and linear momentum has dimensional formula - [MLT-¹]
In option c), work is given by the formula force*distance and energy is given by the formula mass*acceleration due to gravity*height.
Hence, they have same dimensional formula - [ML²T-²].
In option d), acceleration has formula rate of change of velocity per unit time.
Hence, acceleration has dimensional formula - [LT-²] and velocity has dimensional formula - [LT-¹].