Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm.

Reason R :

Least Count = $${{Pitch} \over {Total\,divisions\,on\,circular\,scale}}$$

In the light of the above statements, choose the most appropriate answer from the options given below :

A body takes 4 min. to cool from 61$$^\circ$$ C to 59$$^\circ$$ C. If the temperature of the surroundings is 30$$^\circ$$ C, the time taken by the body to cool from 51$$^\circ$$ C to 49$$^\circ$$ C is :

Consider an electrical circuit containing a two way switch 'S'. Initially S is open and then T₁ is connected to T₂. As the current in R = 6$$\Omega$$ attains a maximum value of steady state level, T₁ is disconnected from T₂ and immediately connected to T₃. Potential drop across r = 3$$\Omega$$ resistor immediately after T₁ is connected to T₃ is __________ V. (Round off to the Nearest Integer)

Suppose two planets (spherical in shape) in radii R and 2R, but mass M and 9M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'v' required for the satellite to reach the surface of the second planet is $$\sqrt {{a \over 7}{{GM} \over R}} $$ then the value of 'a' is ____________.

[Given : The two planets are fixed in their position]