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WORK ENERGY AND POWER Quiz-20

Dear Readers,

Work power energy is the most important chapter when it comes to mechanics, for JEE (Advanced). The chapter is quite tricky and takes a lot of time and devotion on your part to understand and master. But this chapter is a complete gold medal for almost all the questions of the mechanics can be solved by the work power energy approach if you master this topic..

Q1.
Statement 1: Mountain roads rarely go straight up the slope 
 Statement 2:Slope of mountains are large therefore more chances of vehicle to slip from roads
  •  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is False
  •  Statement 1 is False, Statement 2 is True
Solution
If roads of the mountain were to go straight up, the slope θ would have been large, the frictional force μmg cos⁡θ would be small. Due to small friction, wheels of vehicle would slip. Also for going up a large slope, a greater power shall be required


Q2.
Statement 1:If a light body and heavy body have equal kinetic energies, momentum is greater for the heavy body. 
Statement 2: If a light body and heavy body have same momentum, the light body will possess more kinetic energy.
  •  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is False
  •  Statement 1 is False, Statement 2 is True
Solution
From the formula, K=p^2/2m⇒p^2∝m Thus, if kinetic energy is same for both bodies then momentum will be greater for heavy body. Also if momentum is equal for both the bodies then kinetic energy will be higher for lighter body.


Q3.  
Statement 1: If a spring is compressed, energy is stored in a spring and when it is elongated, energy is released 
  Statement 2:The energy stored in a spring is proportional to the square of linear deformation of spring
  •  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is False
  •  Statement 1 is False, Statement 2 is True
Solution
U=1/2 K(∆x)^2; ∆x may be compression or elongation

Q4. 
Statement 1: Heavy water is used as moderator in nuclear reactor
 Statement 2: Water cools down the fast neutrons
  •  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is False
  •  Statement 1 is False, Statement 2 is True
Solution
When two bodies of same mass undergo an elastic collision, their velocities get interchanged after collision. Water and heavy water are hydrogenic materials containing protons having approximately the same mass as that of a neutron. When fast moving neutrons collide with protons, the neutrons come to rest and protons move with the velocity of that of neutrons


Q5.
Statement 1: A light body and heavy body have same momentum. Then they also have same kinetic energy
 Statement 2: Kinetic energy does not depend on mass of the body
  •  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is False
  •  Statement 1 is False, Statement 2 is True
Solution
 
When two bodies have same momentum then lighter body masses more kinetic energy because E=P^2/2m ∴E∝1/m when P= constant


Q6. 
Statement 1: Work done by or against gravitational force in moving a body from one point to another is independent of the actual path followed between the two points 
Statement 2: Gravitational forces are conservative forces
  •  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is False
  •  Statement 1 is False, Statement 2 is True
Solution
From, definition, work done in moving a body against a conservative force is independent of the path followed


Q7.
Statement 1: In case of bullet fired from gun, the ratio of kinetic energy of gun and bullet is equal to ratio of mass of bullet and gun  
Statement 2: In firing, momentum is conserved
  •  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is False
  •  Statement 1 is False, Statement 2 is True
Solution
E=P^2/2m. In firing momentum is conserved ∴E∝1/m So E_gun/E_bullet =m_bullet/m_gun


Q8.
Statement 1: A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now titled to an angle of 30° with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation 
Statement 2: The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination

  •  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is False
  •  Statement 1 is False, Statement 2 is True
Solution
The coefficient of friction between two surface is independent of angle of inclination of the surface


Q9. 


  •  Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1
  •  Statement 1 is True, Statement 2 is False
  •  Statement 1 is False, Statement 2 is True
Solution
For speed to be minimum at c, the speed at B should be just zero Hence, statement II is the correct explanation of statement I


Q10. 

  •   5s
  •  5√2 s
  •  5/√2 s
  •  2.5 s
Solution

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