First slide

Universal law of gravitation

Question

For central force field :
(1) Torque is zero about the central force field.
(2) Angular momentum is conserved about any point in central force field.
(3) Force is position dependent.
(4) Force is conservative.

Difficult

A

only (1) and (2)
B

only (1), (2) and (4)
C

only (1), (3) and (4)
D

(1), (2), (3) and (4)

Solution

For central force field $\vec{F} = f (r) \hat{r}$
Torque $\vec{τ} = \vec{r} \times \vec{F} = \vec{r} \times f (r) \hat{r} = \vec{0}$
Angular momentum $\vec{τ} = \frac{d \vec{L}}{dt} = \vec{0} \Rightarrow \vec{L} = constant$
Every central force is position dependent and conservative in nature.

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