Answer

Verified

375.3k+ views

**Hint:**We should know that force is the rate of change of momentum and momentum is defined as a product of mass and acceleration. Substituting the values of rate of change of mass as M kg/s and rate of change of velocity as zero we get the desired value of force. Remember force is a vector quantity and so its direction is also to be taken into account.

**Complete step by step answer:**

Given the rate of change of mass with respect to time is M kg/s.

The constant velocity of the conveyor belt is v m/s.

We know that according to Newton's second law of motion, force applied is directly proportional to the change in the momentum(p) and force is in the direction of the change of momentum.

$F=\dfrac{dp}{dt}$ ---------(1)

Momentum is defined as a product of mass and velocity,$p=mv$.

Therefore equation 1 becomes,

$F=\dfrac{d\left( mv \right)}{dt}$

On differentiating we get,

$F=m\dfrac{dv}{dt}+v\dfrac{dm}{dt}$

The rate of change of velocity with time is zero since the velocity is constant.

Substituting the value of rate of change of mass with respect to time is M kg/s.

Therefore we get force as,

$F=m\times 0+vM \\

\therefore F=Mv$

The force necessary to keep the belt moving with a constant velocity of $v\, m/s$ will be $Mv\,N$.

**Hence, option C is correct.**

**Note:**One should know Newton's second law of motion to solve such types of problems, which states that force is directly proportional to the rate of change of momentum, $F=\dfrac{dp}{dt}$. When more than one force acts on any system then we have to add all the forces vectorially using either triangle law of vector addition or parallelogram law of vector addition. If the external force is zero, then the acceleration of the body is zero. Newton’s third law states that forces always occur in pairs.

Recently Updated Pages

Cryolite and fluorspar are mixed with Al2O3 during class 11 chemistry CBSE

Select the smallest atom A F B Cl C Br D I class 11 chemistry CBSE

The best reagent to convert pent 3 en 2 ol and pent class 11 chemistry CBSE

Reverse process of sublimation is aFusion bCondensation class 11 chemistry CBSE

The best and latest technique for isolation purification class 11 chemistry CBSE

Hydrochloric acid is a Strong acid b Weak acid c Strong class 11 chemistry CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Define limiting molar conductivity Why does the conductivity class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Name 10 Living and Non living things class 9 biology CBSE

The Buddhist universities of Nalanda and Vikramshila class 7 social science CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE