Tag: force and newton's laws of motion

Questions Related to force and newton's laws of motion

Two bodies $A$ and $B$ having mass $M$ and $m$ respectively possesses same kinetic energy. Given that $M> m$. If ${\rho} _{A}$ and ${\rho} _{B}$ be their momentum, then which of the following statements is true?

physics force and newton's laws of motion momentum (p) introduction to momentum linear momentum

  1. ${ \rho } _{ A }={ \rho } _{ B }$

  2. ${ \rho } _{ A }> { \rho } _{ B }$

  3. ${ \rho } _{ A }< { \rho } _{ B }$

  4. It cannot be predicted

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Correct Option: C
Explanation:
Two bodies A and B having mass m and M respectively possesses same Kinetic energy : 
$K _A = K _B$
In general kinetic energy, $K = \dfrac{1}{2} mv^2 = \dfrac{p^2}{2m}$ where $p$ is momentum. 
$\therefore \dfrac{\rho _A ^2}{2M} = \dfrac{\rho _B ^2}{2m}$
$ \dfrac{\rho _A ^2}{M} = \dfrac{\rho _B ^2}{m}$
But $M>m$ and therefore for above equation to be true $\rho _A ^2 < \rho _B ^2$ or $\rho _A < \rho _B $ 

For constant non zero mass, momentum versus velocity graph is a:

physics force and newton's laws of motion momentum (p) introduction to momentum linear momentum

  1. straight line parallel to x- axis

  2. straight line parallel to y- axis

  3. straight line passing through origin

  4. straight line passing through y- axis with an intercept

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Correct Option: C
Explanation:

We know that,
Momentum = mass $ \times $ velocity
So, we know that when a graph is plotted, momentum against velocity, it is a straight line passing through the origin because momentum varies linearly with respect to velocity.

A body of mass $2 kg$ is sliding with a constant velocity of $4 m/s$ on a frictionless horizontal table. The net force required to keep the body moving with the same velocity is

physics force and newton's laws of motion momentum (p) introduction to momentum linear momentum

  1. $8 N$

  2. $0 N$

  3. $4 N$

  4. $\dfrac { 1 }{ 2 }  N$

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Correct Option: B
Explanation:

According to newton's first law of motion, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external net force.
Therefore The force required to keep the body moving with the same velocity is zero.