Units and Measu...

Write the dimensions of $$a \times b$$ in the relation. $$E = \dfrac{b - x^2}{at}$$, where $$E$$ is the energy, $$x$$ is the displacement, and $$t$$ is the time.

The percentage errors in the measurement of mass and speed are $$2\%$$ and $$3\%$$, respectively. How much will be the maximum error in the estimation of KE obtained by measuring mass and speed?

The mass of the liquid flowing per second per unit area of cross section of the tube if proportional to $$P^x$$ and $$v^y$$, where $$P$$ is the pressure difference and $$v$$ is the velocity then the relation between $$x$$ and $$y$$ is

If frequency $$F$$, velocity $$V$$, and density $$D$$ are considered fundamental units, the dimensional formula for momentum will be

If the velocity of light $$C$$, the universal gravitational constant $$G$$, and Planck's constant $$h$$ are chosen as fundamental units, the dimension of mass in this system are

The number of significant figures in $$5.69 \times 10^{15}$$kg is

The potential energy of a particle varies with distance $$x$$ as $$U = \dfrac{Ax^{1/2}}{x^2 + B}$$, where A and B are constants. The dimensional formula for A x B is:

The time dependence of a physical quantity $$P$$ is given by $$P = P_0e^{-\alpha t^2}$$, where $$\alpha$$ is a constant and t is time. Then constant $$\alpha$$ is / has

The position x of a particle at time t is given by $$x = \dfrac{V_0}{a}(1 - e^{-at})$$, where $$V_0$$ is constant and $$a > 0$$. The dimensions of $$V_0$$ and $$a$$ are

The specific resistance $$\rho$$ of a circular wire of radius r, resistance R, and length l is given by $$\rho = \pi r^2 R/l$$. Given: $$r = 0.24\pm 0.02 cm, R = 30 \pm 1 \Omega,$$ and $$l=4.80\pm 0.01cm.$$ The percentage error in $$\rho$$ is nearly: