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 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 \(M^0L^0T^1\).
The dimensional formula of angular momentum is:
[1988]
Angular momentum is defined as \(L = r \times p\), where \(r\) is distance and \(p\) is linear momentum. Its dimensions are \([L][MLT^{-1}] = [ML^2T^{-1}]\).
The dimension of Planck constant equals to that of:
[2001]
Planck's constant \(h\) has dimensions \(ML^2T^{-1}\). Angular momentum also has dimensions \(ML^2T^{-1}\).
Turpentine oil is flowing through a tube of length (l) and radius (r). The pressure difference between the two ends of the tube is (P). The viscosity of oil is given by \(\eta = \frac{P(r^2 – x^2)}{4vl}\) where (v) is the velocity of oil at a distance (x) from the axis of the tube. The dimensions of (eta) are:
[1993]
\([P] = [ML^{-1}T^{-2}]). ([r^2 - x^2] = [L^2]\). \([v] = [LT^{-1}]\). \([l] = [L]\). \([\eta] = \frac{[ML^{-1}T^{-2}][L^2]}{[LT^{-1}][L]} = \frac{[MLT^{-2}]}{[L^2T^{-1}]} = [ML^{-1}T^{-1}]\).