Units and Measu...

Dimension of $$\epsilon_0$$ are

Which of the following is dimensionally incorrect ?

The dimensions of energy per unit volumes are the same as those of :

If temperature of sun is decreased by $$1\%$$ then the value of solar constant will change by

Pressure P varies as $$P=\cfrac { \alpha  }{ \beta  } exp\left( \cfrac { -\alpha  }{ { K }_{ B }\theta  } Z \right) $$ where Z denotes distance. $${ K }_{ B }$$ Boltzman's constant.$$\theta $$ temperature and $$\alpha ,\beta$$ are constants.Derive the dimensions of $$\beta $$

The dimensional formula of angular velocity $$\left(\omega=\cfrac{v}{r}\right)$$ is

Pressure P varies as $$P=\dfrac{\alpha}{\beta}$$ exp$$(\dfrac{-\alpha}{K_B \theta}Z)$$ where Z denotes distance,$$K_B$$ Boltzman's constant,$$\theta$$ absolute temperature and $$\alpha,\beta$$ are constants.Derive the dimensions of $$\beta$$

If there is a positive error of $$50\%$$ in the measurement of velocity of a body, then the error in the measurement of kinetic energy is :

A student uses a metre scale, measuring upto $$1\ mm$$, to measure the length an breadth of a retangular plate. He finds that length$$=5.7\ cm$$ and breadth $$=3.4\ cm$$. What is the percentage error in the area of the plate?

A dimensionless quantity :