The equation of motion $s = ut + \frac{1}{2}at^2$ is derived assuming what condition for acceleration?

What is dimensional formula of thermal conductivity?

A particle is projected with velocity $v_0$ at an angle $heta$ with the horizontal. At the highest point of its trajectory, it explodes into two fragments of masses $m_1$ and $m_2$. The lighter fragment $m_1$ falls vertically downwards with zero initial speed. If the range of the original projectile was $R$, the distance from the point of projection where the heavier fragment lands is:

A projectile is launched with an initial velocity 'u' at an angle $heta$ with the horizontal. Derive an expression for the maximum height reached by the projectile.

A rectangular beam which is supported at its two ends and leaded in the middle with weight w sags by an amount δ such that $\delta = \frac{{w{l^3}}}{{4Y{d^3}}},\;$, where $l,d$ and Y represent length, depth and elasticity respectively. Guess the unknown factor using dimensional considerations

Two quantities A and B are related by the relation $\frac{A}{B}$=m, where m is linear mass den sity and A is force. The dimensions of B will be

Position of body with acceleration ‘a’ is given by $x = K{a^m}{t^n}$ , here t is time. Find dimensions of m and n

A lens has a focal length 'f'. Derive the lens maker's formula, relating f to the refractive index 'n' of the lens material and the radii of curvature $R_1$ and $R_2$ of its surfaces.

Universal time is based on

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

The dimensions of ${e^2}/4{\rm{\pi }}{{\rm{\varepsilon }}_0}hc,$, where $e,\;{{\rm{\varepsilon }}_0},{\rm{\;}}h\;{\rm{and\;}}c$ are electronic charge, electric permittivity, Planck’s constant and velocity of light in vacuum respectively, are