Question

Match the following question:

Column 1	Column 2
Acceleration due to gravity($g$)	vector quantity
Gravitational constant($G$)	$F=\frac{GMm}{r^2}$
Force of gravitation	Scalar quantity
Weight	$9.8m/s^2$

Answer 1

Part-A:

The acceleration due to gravity of Earth, denoted by $g$, is the net acceleration that is imparted to objects due to the combined effect of gravitation and centrifugal force. It is a vector quantity, whose direction coincides with a plumb bob and strength or magnitude. The value of acceleration due to gravity is $9.8m/s^2$.

Thus,(A)-(IV)

Part-B:

A vector quantity is a quantity that has both magnitude and direction but a scalar quantity possesses only magnitude. A Gravitational constant is a scalar quantity as it has magnitude but not direction and also it does not follow the law of addition of vectors.

Thus,(B)-(III)

Part-C:

Newton's law of universal gravitation states that every point mass attracts every other point mass by a force acting along the line intersecting the two points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

Force of gravitation is given by $F=\frac{GMm}{r^2}$.

where F is the gravitational force acting between two objects, m₁ and m₂ are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant.

Thus,(C)-(II)

Part-D:

Weight can be expressed as W=mg, where m is the mass of the object and g is the acceleration due to gravity. So, Weight can be defined as a force with direction towards the centre of the planet. Weight has both magnitude and direction. Hence, weight is a vector quantity. Weight is a vector quantity because it has both magnitude and direction.

Thus,(D)-(I)

Hence, (A)-(IV), (B)-(III), (C)-(II), (D)-(I). The above answers are correctly matched.