Answer
414.6k+ views
Hint: The force required to hold the ball at its place by the batsman is equal to the difference of final momentum and initial momentum divided by the time. The product of mass and velocity is called momentum.
Complete step by step answer:A cricket ball of mass m is 150g = 0.150 Kg(1g = 0.001Kg) moving with a speed u of 126 km/h hits the bat. The collision between them is completely elastic and the two remain in contact for time t=0.001s. The ball moves back with the same velocity as the collision is elastic but in an opposite direction i.e., v=-u.
We change the velocity from km/h to m/s, velocity = $126 \times \dfrac{5}{{18}} = 35m{s^{ - 1}}\left[ {1km{h^{ - 1}} = \dfrac{5}{{18}}m{s^{ - 1}}} \right]$
Force applied by the batsman (F)= Rate of change of momentum
\[F = \dfrac{{{\text{ }}\left( {Final{\text{ }}momentum{\text{ }} - \;Initial{\text{ }}momentum} \right)}}{{time}}\]
$F = \dfrac{{\left( {mv - mu} \right)}}{t}$
$F = \dfrac{{m\left( { - u} \right) - mu}}{t}$
$F = \dfrac{{ - mu - mu}}{t}$
$F = \dfrac{{ - 2mu}}{t}$
$F = \dfrac{{ - 2 \times 0.15 \times 35}}{{0.001}}$
$F = - 10500N = - 1.05 \times {10^4}N$
Hence, the force that the batsman has to apply to hold the bat firmly at its place is $1.05 \times {10^4}$N and its direction is negative as compared to the direction of the ball.
Therefore, option C is correct.
Note:The force applied by the batsman is equal to the rate of change of momentum because the necessary force required to hold the ball at this place for 0.001s is provided by the momentum of the ball and its sign is negative as it is in an opposite direction to that of a ball.
Complete step by step answer:A cricket ball of mass m is 150g = 0.150 Kg(1g = 0.001Kg) moving with a speed u of 126 km/h hits the bat. The collision between them is completely elastic and the two remain in contact for time t=0.001s. The ball moves back with the same velocity as the collision is elastic but in an opposite direction i.e., v=-u.
We change the velocity from km/h to m/s, velocity = $126 \times \dfrac{5}{{18}} = 35m{s^{ - 1}}\left[ {1km{h^{ - 1}} = \dfrac{5}{{18}}m{s^{ - 1}}} \right]$
Force applied by the batsman (F)= Rate of change of momentum
\[F = \dfrac{{{\text{ }}\left( {Final{\text{ }}momentum{\text{ }} - \;Initial{\text{ }}momentum} \right)}}{{time}}\]
$F = \dfrac{{\left( {mv - mu} \right)}}{t}$
$F = \dfrac{{m\left( { - u} \right) - mu}}{t}$
$F = \dfrac{{ - mu - mu}}{t}$
$F = \dfrac{{ - 2mu}}{t}$
$F = \dfrac{{ - 2 \times 0.15 \times 35}}{{0.001}}$
$F = - 10500N = - 1.05 \times {10^4}N$
Hence, the force that the batsman has to apply to hold the bat firmly at its place is $1.05 \times {10^4}$N and its direction is negative as compared to the direction of the ball.
Therefore, option C is correct.
Note:The force applied by the batsman is equal to the rate of change of momentum because the necessary force required to hold the ball at this place for 0.001s is provided by the momentum of the ball and its sign is negative as it is in an opposite direction to that of a ball.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)