Home
Class 12
PHYSICS
A uniform solid right circular cone of b...

A uniform solid right circular cone of base radius `R` is joined to a uniform solid hemisphere of radius `R` and of the same density, as shown. The centre of mass of the composite solid lies at the centre of base of the cone. The height of the cone is

A

1.5R

B

`sqrt(3)R`

C

3R

D

`2sqrt(3)R`

Text Solution

Verified by Experts

The correct Answer is:
B
`((1)/(3)piR^(2)h)pxx(h)/(4)=((2)/(3)piR^(3))p(3R)/(8)`
`h=sqrt(3)R`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    ALLEN|Exercise PAPER 2|60 Videos

  • TEST PAPERS

    ALLEN|Exercise PAPER 3|100 Videos

  • TEST PAPER 4

    ALLEN|Exercise PHYSICS|45 Videos

  • UNIT & DIMENSIONS, BASIC MATHS AND VECTOR

    ALLEN|Exercise Exercise (J-A)|7 Videos

Similar Questions

Explore conceptually related problems

A uniform solid right circular cone of base radius R is joined to a uniform solid hemisphere of radius R and of the same density, so as to have a common face. The centre of mass of the composite solid lies on the common face. The height of the cone is:

Find the centre of mass of a uniform solid cone.

The centre of mass of a solid cone along the line form the center of the base to the vertex is at

A right circular cone of radius R and height 2 R is placed on a hemisphere of radius R . Locate c.m. of the combined mass from O .

A uniform solid cone of height 40 cm is shown in figure. The distance of centre of mass of the cone from point B (centre of the base) is :

A uniform solid cone of height 40 cm is shown in figure. The distance of centre of mass of the cone from point B (centre of the base) is :

A solid metallic sphere of radius 6.3 cm is melted and recast into a right circular cone of height 25.2 cm. What is the ratio of the diameter of the base to the height of the cone ?

ALLEN-TEST PAPERS-MATHS
  1. A uniform solid right circular cone of base radius R is joined to a un...

    Text Solution

    |

  2. If complex number z(zne2) satisfies the equation z^(2)=4z+|z|^(2)+(16)...

    Text Solution

    |

  3. Let omegabe a complex number which satisfies iomega=(u^(2)-1)/(u^(2)+...

    Text Solution

    |

  4. If the function f(x)={{:((1+cospix)/(pi^(2)(x+1)^(2)),",",xlt-1),(ax...

    Text Solution

    |

  5. The value of the following limit lim(ntooo) n(n+1)(ln(1+(1)/(n))-sin((...

    Text Solution

    |

  6. number of solutions for x between 3 and 15 if int(0)^(x)[t]dt=int(0)^(...

    Text Solution

    |

  7. If the length of perpendicular from (0,0,0) to the plane ax+by+cz+d=0 ...

    Text Solution

    |

  8. A transversal cuts side AB and AD and diagonal AC of parallelogram ABC...

    Text Solution

    |

  9. Consider curve y=(1+x)^(y)+sin^(-1)(sin^(2)x). Which of the following ...

    Text Solution

    |

  10. The x-intercept of the tangent to a curve is equal to the ordinate of ...

    Text Solution

    |

  11. Suppose y=f(x)andy=g(x) are two functions whose graph intersect at th...

    Text Solution

    |

  12. A function y=f(x) satisfies f"(x)=-(1)/(x^(2))-pisin(pix),f(2)=pi+(1)...

    Text Solution

    |

  13. Let(1+X^(2))^(2)(1+X)^(n)=sum(k=0)^(n+4)a(k)X^(k).ifa(1),a(2),a(3) ar...

    Text Solution

    |

  14. If f(x) is double differentiable function such that |f"(x)|le5 for ea...

    Text Solution

    |

  15. overline(x)andoverline(y) be two variable vectors satisfying simultan...

    Text Solution

    |

  16. The curve defined by sqrt((x)/(a))+sqrt((y)/(b))=1 gives a part of pa...

    Text Solution

    |

  17. The curve defined by sqrt((x)/(a))+sqrt((y)/(b))=1 gives a part of pa...

    Text Solution

    |

  18. In a problem of differentiation of (f(x))/(g(x)), one student writes ...

    Text Solution

    |

  19. In a problem of differentiation of (f(x))/(g(x)), one student writes ...

    Text Solution

    |