The time period ($T$) of a simple pendulum depends on its length ($l$) and acceleration due to gravity ($g$). Which of the following is dimensionally consistent with the principle of homogeneity?

The unit of angular acceleration in the SI system is

The time period of a simple pendulum is given by $T = 2\pi\sqrt{\frac{l}{g}} + kx$, where $l$ is the length, $g$ is acceleration due to gravity, and $x$ is displacement. The dimensions of $k$ are:

If ${u_1}\,and\,{u_2}$ are the units selected in two systems of measurement and ${n_1}\,and\,{n_2}$ their numerical values, then

Which one of the following is not a unit of Young’s modulus?

Which of the following is not equal to watt

Wavelength of ray of light is 0.00006 m. It is equal to

In an experiment the angles are required to be measured using an instrument. 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a-degree $\left( { = 0.5^\circ } \right),$ then the least count of the instrument is

Precision in measurement depends on

The velocity of a wave is given by $v = \sqrt{\frac{T}{\mu}} + ax^2$, where $T$ is tension, $\mu$ is linear density, and $x$ is displacement. What are the dimensions of $a$?

Length is measured in metre and time in second as usual. But a new unit of mass is so chosen that G=1. This new unit of mass is equal to