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In a typical combustion engine the work done by a gas molecule is given $W =\alpha^{2} \beta e ^{\frac{-\beta x ^{2}}{ KT }}$, where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature. If $\alpha$ and $\beta$ are constants, dimensions of $\alpha$ will be
The potential energy $u$ of a particle varies with distance $x$ from a fixed origin as $u=\frac{A \sqrt{x}}{x+B}$, where $A$ and $B$ are constants. The dimensions of $A$ and $B$ are respectively
Planck's constant $(h),$ speed of light in vacuum $(c)$ and Newton's gravitational constant $(G)$ are three fundamental constants. Which of the following combinations of these has the dimension of length $?$
If the constant of gravitation $(G)$, Planck's constant $(h)$ and the velocity of light $(c)$ be chosen as fundamental units. The dimension of the radius of gyration is
The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively $4\%$ and $2\%$, The maximum error in the measurement of pressure is ....... $\%$