In a vernier callipers, $21$ divisions on the vernier scale coincide with $20$ divisions on the main scale. If each division on the main scale is $0.5$ mm, find the vernier constant (in cm).

If the velocity $v\left( {{\rm{is\;cm}}{{\rm{s}}^{ - 1}}} \right)$ of a particle is given in terms of t (in second) by the relation $\;\;v = at + \frac{b}{{t + c}}$ then, the dimensions of a,b and c are

In a vernier callipers, $21$ divisions on the vernier scale coincide with $20$ divisions on the main scale. If each division on the main scale is $0.5$ mm, find the vernier constant (in cm).

In a vernier callipers, $(N+3)$ divisions of vernier scale coincide with $N$ divisions of the main scale. If 1 MSD represents $0.1$ mm, the vernier constant (in cm) is:

If $N$ divisions on a vernier scale coincide with $(N-2)$ divisions on the main scale, and each main scale division represents $1$ mm, what is the vernier constant of the callipers (in cm)?

Which of the following cannot be determined using dimensional analysis?

If the velocity $v\left( {{\rm{is\;cm}}{{\rm{s}}^{ - 1}}} \right)$ of a particle is given in terms of t (in second) by the relation $\;\;v = at + \frac{b}{{t + c}}$ then, the dimensions of a,b and c are

Dimensional analysis cannot be used to derive relationships containing:

The relative density of the material of a body is the ratio of its weight in air and the loss of its weight in water. By using a spring balance, the weight of the body in air in measured to be 5.00 $\pm$ 0.05N. The weight of the body in water is measured to be 4.00 $\pm$ 0.05N. Then the maximum possible percentage error in relative density is

Which of these equations, though dimensionally correct, might be physically incorrect due to limitations of dimensional analysis?

Dimensional analysis fails to determine the formula for a physical quantity if it depends on: