Home
Class 12
PHYSICS
Assertion: Two particles of different ma...

Assertion: Two particles of different mass, projected with same velocity at same angles. The maximum height attained by both the particle will be same.
Reason: The maximum height of projetile is independent of particle mass.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the given question, we will analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: The assertion states that two particles of different masses, when projected with the same velocity at the same angle, will attain the same maximum height. 2. **Understanding the Reason**: The reason given is that the maximum height of a projectile is independent of the mass of the particle. 3. **Formula for Maximum Height**: The maximum height (h_max) attained by a projectile can be calculated using the formula: \[ h_{max} = \frac{u_y^2}{2g} \] where \( u_y \) is the vertical component of the initial velocity, and \( g \) is the acceleration due to gravity. 4. **Calculating the Vertical Component**: The vertical component of the initial velocity can be expressed as: \[ u_y = u \sin \theta \] where \( u \) is the initial velocity and \( \theta \) is the angle of projection. 5. **Substituting into the Formula**: Substituting \( u_y \) into the maximum height formula gives: \[ h_{max} = \frac{(u \sin \theta)^2}{2g} = \frac{u^2 \sin^2 \theta}{2g} \] 6. **Independence from Mass**: From the formula derived, we can see that the maximum height \( h_{max} \) depends only on the initial velocity \( u \), the angle \( \theta \), and the acceleration due to gravity \( g \). Notably, there is no mass term in this equation, which indicates that the maximum height is indeed independent of the mass of the projectile. 7. **Conclusion**: Since both the assertion and reason are true, and the reason correctly explains the assertion, we conclude that the assertion is true, the reason is true, and the reason is the correct explanation for the assertion. ### Final Answer: - Statement 1 (Assertion) is true. - Statement 2 (Reason) is true. - Statement 2 is the correct explanation for Statement 1.

To solve the given question, we will analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: The assertion states that two particles of different masses, when projected with the same velocity at the same angle, will attain the same maximum height. 2. **Understanding the Reason**: ...
Promotional Banner

Topper's Solved these Questions

  • Motion in Two Dimensions

    VMC MODULES ENGLISH|Exercise JEE Main (Archive)|19 Videos
  • Motion in Two Dimensions

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|19 Videos
  • Motion in Two Dimensions

    VMC MODULES ENGLISH|Exercise Long Answer Type|5 Videos
  • Motion in Straight Line

    VMC MODULES ENGLISH|Exercise IN-CHAPTER EXERCISE-J|10 Videos
  • MOVING CHARGES & MAGNETISM

    VMC MODULES ENGLISH|Exercise IN-CHAPTER EXERCISE-K|10 Videos

Similar Questions

Explore conceptually related problems

Maximum height attained from the point of projection is:

Two particles are projected with same velocity but at angles of projection 35° and 55°. Then their horizontal ranges are in the ratio of

Two particle are projected with same initial velocities at an angle 30^(@) and 60^(@) with the horizontal .Then

Two particles are projected with same velocity but at angles of projection 25° and 65° with horizontal. The ratio of their horizontal ranges is

Two bodies of same mass are projected with the same velocity at an angle 30^(@) and 60^(@) respectively.The ration of their horizontal ranges will be

Assertion If a particle is projected vertically upwards with velocity u, the maximum height attained by the particle is h_(1) . The same particle is projected at angle 30^(@) from horizontal with the same speed u. Now the maximum height is h_(2) . Thus h_(1) = 4h_(2) . Reason In first case, v =0 at highest point and in second case v ne 0 at highest point.

A proton and an alpha particle projected with same velocity in uniform transverse magnetic field then

A particle is projected with a velocity 10 m//s at an angle 37^(@) to the horizontal. Find the location at which the particle is at a height 1 m from point of projection.

A particle is thrown vertically upwards. If its velocity is half of the maximum height is 20 m//s , then maximum height attained by it is

The following particles are moving with the same velocity. Which particle has maximum momentum ?

VMC MODULES ENGLISH-Motion in Two Dimensions-Level -1
  1. Average velocity of a particle in projectile motion between its starti...

    Text Solution

    |

  2. In a projectile motion the velocity

    Text Solution

    |

  3. Assertion: Two particles of different mass, projected with same veloci...

    Text Solution

    |

  4. The horizontal and vertical displacements x and y of a projectile at a...

    Text Solution

    |

  5. The equation of a projectile is y=sqrt(3)x-(gx^(2))/(2) the angle of...

    Text Solution

    |

  6. A ball is hit by a batsman at an angle of 37^(@) as shown in figure. T...

    Text Solution

    |

  7. A boy throws a ball with a velocity u at an angle theta with the horiz...

    Text Solution

    |

  8. Two bullets are fired simultaneously, horizontally but with different ...

    Text Solution

    |

  9. A glass marble projected horizontally from the top of a table falls at...

    Text Solution

    |

  10. A bomber moving horizontally with 500m//s drops a bomb which strikes g...

    Text Solution

    |

  11. A body is projected horizontally from a very high tower with speed 20...

    Text Solution

    |

  12. A ball rolls off the top of a staircase with a horizontal velocity u m...

    Text Solution

    |

  13. An acroplane is flying horizontally with a velocity of 600 km/h and a...

    Text Solution

    |

  14. From the top of a tower of height 40m, a ball is projected upward with...

    Text Solution

    |

  15. In previous question, what is the relation between h1 and h2

    Text Solution

    |

  16. A cannon on a level plane is aimed at an angle alpha above the horizon...

    Text Solution

    |

  17. A body is projected horizontally from a point above the ground. The mo...

    Text Solution

    |

  18. A particle is thrown at time t = 0 with a velocity of 10 ms^(-1) at an...

    Text Solution

    |

  19. A ball is projected horizontally with a speed v from the top of the pl...

    Text Solution

    |

  20. A ball is thrown horizontally from a point O with speed 20 m/s as show...

    Text Solution

    |