Imagine a box sitting on a shelf. what forces are acting on the box?

a. both gravity and normal

b. normal

c. gravity

d. none of the answers are correct

In case of an object sitting at rest on another base, there are two equal and opposite forces – Normal force and the gravity.

Option A

Explanation:

When an object is placed at rest position on another object, there is a force exerted by the surfaces of the two contact objects. This force is denoted as Normal Force.

When an object such as a box is placed on a shelf, its surface exerts a contact force on the base of the shelf- The Normal force directed upward. Meanwhile, the gravity stays at its action and tries to pull the box towards itself.  

Both of these forces however are equal and opposite and therefore, there is zero net force on the box. That's why it remains at rest, holding on Newton's third law.

t = 1.4 days

Explanation:

The law of radioactive decay gives the amount of radioactive substance, left after a certain amount of time has passed. The formula of law of radioactive decay is given as follows:

N = N₀ (e)^-λt

where,

λ = decay constant = 0.16

N₀ = Initial Amount of the Substance

N = The Amount of Substance Left after Decay = 80% of N₀ = 0.8 N₀

t = Time Required by the Substance to decay to final value = ?

Substituting these values in the law of radioactive decay formula, we get:

0.8 N₀ = N₀ (e)^-0.16 t

0.8 = (e)^-0.16 t

ln (0.8) = -0.16 t

t = - 0.2231/-0.16

t = 1.4 days