Medium
State whether the following statements are true or false:
$(a)$ $A$ physical quantity can have units but still be dimensionless.
$(b)$ Impulse and the gradient of energy have the same units.
$(c)$ The absolute error in every measurement is equal to the least count of the measuring instrument.
$(a)$ $A$ physical quantity can have units but still be dimensionless.
$(b)$ Impulse and the gradient of energy have the same units.
$(c)$ The absolute error in every measurement is equal to the least count of the measuring instrument.
(A) True. For example,plane angle is measured in radians but is dimensionless.
$(b)$ False. The unit of impulse is $N \cdot s$ (or $kg \cdot m/s$). The unit of the gradient of energy (force) is $N$ (or $kg \cdot m/s^2$). They are not the same.
$(c)$ True. By convention,the absolute error in a single measurement is taken as the least count of the measuring instrument.
$(b)$ False. The unit of impulse is $N \cdot s$ (or $kg \cdot m/s$). The unit of the gradient of energy (force) is $N$ (or $kg \cdot m/s^2$). They are not the same.
$(c)$ True. By convention,the absolute error in a single measurement is taken as the least count of the measuring instrument.
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