Correct Answer - Option 4 : 27 N
The correct answer is option 4) i.e. 27 N
CONCEPT:
-
Acceleration due to gravity on the surface of Earth of mass M and radius Re is denoted by g.
- It has an approximated uniform value of 9.8 m/s2 on the surface of Earth.
The acceleration due to gravity at a depth 'd' below the surface of Earth is given by
\(\Rightarrow g' = g(1- \frac{d}{R_e})\)
- The acceleration due to gravity at a height 'h' above the surface of Earth is given by
\(\Rightarrow g'' = g(1+ \frac{h}{R_e})^{-2}\)
-
Weight: Weight is defined as the force with which an object is pulled towards the Earth due to gravity.
It is given by:
Weight, W = mg
Where m is the mass of the object and g is the acceleration due to gravity.
CALCULATION:
Given that:
Weight of the object on Earth, W = 432 N = mg ----(1)
Acceleration due to gravity at height h = 3R from the surface of Earth, \(g'' = g(1+ \frac{h}{R_e})^{-2}\)
\(\Rightarrow g'' = g(1+ \frac{3R}{R})^{-2} = g (4)^{-2} = \frac{g}{16} \: m/s^2\)
Using, W = mg
The weight of the box at 3R, \(W'' = mg''= m\times \frac{g}{16} = \frac{W}{16} \) ----(2)
Substituting (1) in (2),
\(W'' =\frac{423}{16} = 27\: N\)
