Plane angle and solid angle have:
[2022]
Plane angle (radian) and solid angle (steradian) are dimensionless quantities (ratios of lengths or areas) but possess units.
Dimensions of stress are:
[2020]
Stress is Force per unit Area. \([\text{Stress}] = [F]/[A] = (MLT^{-2})/L^2 = ML^{-1}T^{-2}\).
The dimension of Planck constant equals to that of:
[2001]
Planck's constant \(h\) has dimensions \(ML^2T^{-1}\). Angular momentum also has dimensions \(ML^2T^{-1}\).
Which of the following dimensions will be the same as that of time?
[1996]
The ratio \(L/R\) has the dimensions of time, \(T\).
Which of the following is a dimensional constant?
[1995]
A dimensional constant is a physical constant with dimensions. The Gravitational constant \(G\) is a dimensional constant with dimensions \(M^{-1}L^3T^{-2}\).
The dimensions of \(RC\) is:
[1995]
The product \(RC\) represents the time constant of an \(RC\) circuit, and its dimension is time, \(T\).
Which of the following has the dimensions of pressure?
[1994,90]
Pressure is defined as Force per unit Area. Its dimensions are \(MLT^{-2} / L^2 = ML^{-1}T^{-2}\).
Dimensional formula of self inductance is:
[1989]
The energy stored in an inductor is \(U = \frac{1}{2}LI^2\). Therefore, the dimensions of self-inductance \(L\) are \(U/I^2 = [ML^2T^{-2}]/[A^2] = [ML^2T^{-2}A^{-2}]\).
The dimensional formula of torque is:
[1989]
Torque is calculated as Force \(\times\) perpendicular distance. So its dimensions are \([MLT^{-2}] \times [L] = [ML^2T^{-2}]\).
If \(C\) and \(R\) denote capacitance and resistance, the dimensional formula of \(CR\) is:
[1988]
The product \(CR\) is the time constant of an RC circuit. Its dimension is time, \(T\), which can be written as \(M^0L^0T^1\).