The equation for kinetic energy ($KE = \frac{1}{2}mv^2$) is derived using which fundamental equations?

The Martians use force (F), acceleration (A) and time (T) as their fundamental physical quantities. The dimensions of length on Martians system are

A screw gauge gives the following readings when used to measure the thickness of a metal sheet: Main scale reading: 0 mm, Circular scale reading: 48 divisions. Given that 1 mm on the main scale corresponds to 100 divisions on the circular scale. What is the thickness of the metal sheet?

Universal time is based on

If C is the restoring couple per unit radian twist and I is the moment of inertia, then the dimensional representation of $2{\rm{\pi }}\sqrt {\frac{I}{C}}$ will be

The dimension of magnetic field in M, L, T and C (coulomb) is given as

Derive the expression for the escape velocity of an object from the surface of a planet of mass 'M' and radius 'R'.

A rod of length $L$ is hinged at one end and is free to rotate in a vertical plane. It is released from rest in the horizontal position. The angular acceleration of the rod when it makes an angle $heta$ with the vertical is:

Universal time is based on

A spectrometer gives the following reading when used to measure the angle of a prism

Main scale reading : 58.5 degree

Vernier scale reading : 09 divisions

Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data

Which equation is derived from the definition of acceleration?