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:

The circular scale of a screw gauge having a pitch of 1.0 mm is divided into 100 divisions. When measuring the diameter of a thin rod, the main scale reading is 1 mm and the circular scale reading is 25 divisions. What is the diameter of the rod?

A quantity X is given by ${\varepsilon _0}L\frac{{\Delta V}}{{\Delta t}},\;$, where ${\varepsilon _0}$ is the permittivity of free space, L is a length, ${\Delta V}$ is a potential difference and ${\Delta t}$ is a time interval. The dimensional formula for X is the same as that of

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?

If velocity (v), time (T) and mass (M) are taken as fundamental quantities, then dimensional formula for gravitational potential would be.

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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 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

A particle moves in a plane with a velocity given by $\vec{v} = (A\omega cos(\omega t))\hat{i} + (B\omega sin(\omega t))\hat{j}$. If the particle starts from the origin at $t=0$, the equation of the trajectory is:

If E= energy, G= gravitational constant, I= impulse and M= mass, then dimensions of $\frac{{GI{M^2}}}{{{E^2}}}$ are same as that of

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