   Question Answers

# rate of change of linear momentum is directly proportional to:A. ForceB. AccelerationC. MassD. All  Hint: Define linear momentum. Obtain the mathematical expression for linear momentum. Rate of change in linear momentum can be found by dividing the change in linear momentum with the change in timer at which the change is made.

As we discussed above the linear momentum that is
$P=mv$
Let assume two linear momentum that is ${{P}_{1}}$ at the velocity of ${{v}_{1}}$ and ${{P}_{2}}$ at the velocity of ${{v}_{2}}$.
Now, we have to find out the difference between these two linear momentums which is $\Delta P$
So, the difference of linear momentum is
$\Delta P={{P}_{1}}-{{P}_{2}}$
Where ${{P}_{1}}$and ${{P}_{2}}$ are $m{{v}_{1}}$ and $m{{v}_{2}}$ respectively.
As we discuss before,
For finding the rate of change of linear momentum we have to differentiate the$\Delta P$ with respect to the time.
$\dfrac{\Delta P}{\Delta t}=\dfrac{m({{v}_{1}}-{{v}_{2}})}{\Delta t}=\dfrac{m\Delta v}{\Delta t}$
Where v is the velocity of the object and m is the mass of the object.
We know that the rate of change of velocity is called acceleration and denoted as ‘a’.
So, in the above formula, we could change the $\dfrac{m\Delta v}{\Delta t}$ as 'ma'.
The formula 'ma' is looking familiar because we know that this is Newton's second law $F=ma$.
So, the rate of change of linear momentum is equal to the force
$\dfrac{\Delta P}{\Delta t}=\dfrac{m\Delta v}{\Delta t}=ma=F$

Note: In physics, we also study another formula of linear momentum that is related to kinetic energy is ${{K}_{E}}=\dfrac{{{P}^{2}}}{2m}$. We can also get the answer through this formula but it will be very lengthy as compared to the above formula that we use. So, we have to check the option first and as per the option, we have to choose the right formula which will give us the right answer in a very easy way.
Here I'm mentioning that all the formulas of momentum will give us an answer but for the right selection of formulas will save our time.

Measuring the Rate of Change of Motion  Conservation of Linear Momentum  CBSE Class 11 Physics Law of Motion Formulas  Newton's Second Law of Motion  Conservation Of Momentum  CBSE Class 11 Physics Systems of Particles and Rotational Motion Formulas  CBSE Class 11 Physics Thermal Properties of Matter Formulas  CBSE Class 11 Physics Mechanical Properties of Solids Formulas  CBSE Class 11 Physics Mechanical Properties of Fluids Formulas  Difference Between Momentum and Inertia  Important Questions for CBSE Class 11 Physics Chapter 5 - Law of Motion  NCERT Books Free Download for Class 11 Physics Chapter 5 - Law of Motion  Important Questions for CBSE Class 11 Physics Chapter 11 - Thermal Properties of Matter  Important Questions for CBSE Class 11 Physics Chapter 7 - Systems of Particles and Rotational Motion  Important Questions for CBSE Class 11 Physics Chapter 9 - Mechanical Properties of Solids  Important Questions for CBSE Class 11 Physics Chapter 10 - Mechanical Properties of Fluids  Important Questions for CBSE Class 12 Physics Chapter 11 - Dual Nature of Radiation and Matter  NCERT Books Free Download for Class 11 Physics Chapter 11 - Thermal Properties of Matter  NCERT Books Free Download for Class 11 Physics Chapter 7 - Systems of Particles and Rotational Motion  Important Questions for CBSE Class 11 Physics  Previous Year Question Paper of CBSE Class 10 English  CBSE Class 12 Physics Question Paper 2020  Previous Year Question Paper for CBSE Class 12 Physics  Previous Year Question Paper for CBSE Class 12 Physics - 2015  Previous Year Question Paper for CBSE Class 12 Physics - 2018  Previous Year Question Paper for CBSE Class 12 Physics - 2014  Previous Year Question Paper for CBSE Class 12 Physics - 2013  Previous Year Question Paper for CBSE Class 12 Physics - 2019  Previous Year Physics Question Paper for CBSE Class 12 - 2017  Physics Question Paper for CBSE Class 12 - 2016 Set 1 C  HC Verma Class 11 Physics Part-1 Solutions for Chapter 9 - Centre of Mass, Linear Momentum, Collision  NCERT Solutions for Class 11 Physics Chapter 5  NCERT Solutions for Class 11 Physics Chapter 5 Law of Motion in Hindi  NCERT Exemplar for Class 11 Physics Chapter 5 - Law of Motion (Book Solutions)  HC Verma Class 11 Physics Part-1 Solutions for Chapter 5 - Newton's Laws of Motion  NCERT Exemplar for Class 11 Physics Chapter 11 - Thermal Properties of Matter (Book Solutions)  NCERT Solutions for Class 11 Physics Chapter 11 Thermal Properties of Matter in Hindi  NCERT Solutions for Class 11 Physics Chapter 7  HC Verma Class 11 Physics Part-1 Solutions for Chapter 7 - Circular Motion  NCERT Exemplar for Class 11 Physics Chapter 7 - Systems of Particles and Rotational Motion (Book Solutions)  