Question:

A cricket ball of mass 150 g150\, g moving with a speed of 126 km/h126 \,km/h hits at the middle of the bat, held firmly at its position by the batsman. The ball moves straight back to the bowler after hitting the bat. Assuming that collision between ball and bat is completely elastic and the two remain in contact for 0.001 s0.001\, s, the force that the batsman had to apply to hold the bat firmly at its place would be

Updated On: Jul 5, 2022
  • 10.5 N10.5 \,N
  • 21 N21 \,N
  • 10.5×104 N10.5 \times 10^4\,N
  • 2.1×104 N2.1 \times 10^4 \,N
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The Correct Option is C

Solution and Explanation

Force =change in momentumtime= \frac{\text{change in momentum}}{\text{time}} =mv−(mv)t=2mvt= \frac{mv-\left(mv\right)}{t} = \frac{2mv}{t} Here m=150 g=0.15 kgm = 150\, g = 0.15\, kg, t=0.001 st = 0.001\, s, v=126 km/h=35 m/sv = 126\, km/h = 35\, m/s =2(0.15 kg)(35 m/s)0.001 s= \frac{2\left(0.15\,kg\right)\left(35\,m/s\right)}{0.001\,s} =10500 N=1.05×104 N= 10500\,N = 1.05 \times10^{4}\,N
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Notes on work, energy and power

Concepts Used:

Work, Energy and Power

Work:

  • Work is correlated to force and the displacement over which it acts. When an object is replaced parallel to the force's line of action, it is thought to be doing work. It is a force-driven action that includes movement in the force's direction.
  • The work done by the force is described to be the product of the elements of the force in the direction of the displacement and the magnitude of this displacement.

Energy:

  • A body's energy is its potential to do tasks. Anything that has the capability to work is said to have energy. The unit of energy is the same as the unit of work, i.e., the Joule.
  • There are two types of mechanical energy such as; Kinetic and potential energy.

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Power:

  • Power is the rate at which energy is transferred, conveyed, or converted or the rate of doing work. Technologically, it is the amount of work done per unit of time. The SI unit of power is Watt (W) which is joules per second (J/s). Sometimes the power of motor vehicles and other machines is demonstrated in terms of Horsepower (hp), which is roughly equal to 745.7 watts.
  • Power is a scalar quantity, which gives us a quantity or amount of energy consumed per unit of time but with no manifestation of direction.