Consider two solid spheres of radii R₁ = 1m, R₂ = 2m and masses M₁ and M₂, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of $${{{M_1}} \over {{M_2}}}$$ is :

Three charged particle A, B and C with charges –4q, 2q and –2q are present on the circumference of a circle of radius d. the charged particles A, C and centre O of the circle formed an equilateral triangle as shown in figure. Electric field at O along x-direction is :

A particle is moving along the x-axis with its coordinate with the time 't' given be
x(t) = 10 + 8t – 3t². Another particle is moving the y-axis with its coordinate as a function of time given by y(t) = 5 – 8t³.
At t = 1s, the speed of the second particle as measured in the frame of the first particle is given as $$\sqrt v $$. Then v (in m/s) is ______.

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.