The figure shows a hemispherical shell. The direction of the gravitational field intensity at point $p$ will be along

Six objects are placed at the vertices of a regular hexagon. The geometric centre of the hexagon is at the origin with objects $1$ and $4$ on the $X$-axis (see figure). The mass of the $k$-th object is $m_k = k^i M |\cos \theta_k|$, where $i$ is an integer, $M$ is a constant with the dimension of mass, and $\theta_k$ is the angular position of the $k$-th vertex measured from the positive $X$-axis in the counter-clockwise sense. If the net gravitational force on a body at the centroid vanishes, the value of $i$ is

In a gravitational field,the gravitational potential is given by $V = -\frac{K}{x} \ (J/kg)$. The gravitational field intensity at point $(2, 0, 3) \ m$ is

Two point masses having mass $m$ and $2m$ are placed at a distance $d$. The point on the line joining the point masses,where the gravitational field intensity is zero,will be at a distance ............

If the distance between the centres of Earth and Moon is $D$ and the mass of Earth is $81$ times that of the Moon,at what distance from the centre of Earth will the gravitational field be zero?

$3$ particles each of mass $m$ are kept at the vertices of an equilateral triangle of side $L$. The gravitational field at the centre due to these particles is