Question

The linear momentum p of a body varies with
time and is given by the equation p = a + bt
where a and b are constants. The net force acting
on the body for a one-dimensional motion is
proportional to
a) b) A constant c)1/t d)t​

Answer 1

$\huge{\bold{\underline{\underline{....Answer....}}}}$

$\huge{\bold{\underline{Given:-}}}$

$\large{\bold{P = a + bt}}$

$\huge{\bold{\underline{Explanation:-}}}$

As you know rate of change of momentum is directly proportional to External Force acting on the object.

For Small interval of time,

$\large{F \propto \frac{dp}{dt}}$

Substituting the values,

$\large{F \propto \frac{d (a + bt)}{dt}}$

Differentiating a constant gives Zero.

$\large{F \propto (0 + b)}$

$\large{F \propto b}$

$\huge{\boxed{\boxed{F \propto b}}}$

So, clearly we can see the force is directly proportional to a constant .

So, Correct option is (b) is proportional to a constant.

Answer 2

$\huge{\underline{\underline{\sf{Answer \colon}}}}$

From the Question,

Linear Momentum of the particle is defined by the function: p = a + bt

From Newton's Second Law of Motion,

• Rate of Change of momentum is directly proportional to the net force

Thus,

$\huge{ \boxed{\boxed{\mathrm{\vec{f } \propto \: \frac{dp}{dt}}}}}$

We Know that,

p = a + bt

Differentiating p w.r.t to t,we get:

$\implies \: \sf{ \vec{f} \propto \: \frac{d(a + bt)}{dt} } \\ \\ \implies \: \boxed{\bold{ \vec{f} \propto \: b}}$

Implies,the net force is directly proportional to a constant_______________(b)