Home
Class 12
PHYSICS
A thin rod of length 6 m is lying along ...

A thin rod of length 6 m is lying along the x-axis with its ends at x=0 and x=6m. Its linear density *mass/length ) varies with x as `kx^(4)`. Find the position of centre of mass of rod in meters.

A

5m

B

3m

C

2m

D

4m

Text Solution

Verified by Experts

The correct Answer is:
A
`x_(cm)=(intxdm)/(intdm)=(int_(0)^(6)x(kx^(4)dx))/(int_(0)^(6)(kx^(4)dx))=(int_(0)^(6)x^(5)dx)/(int_(0)^(6)x^(4)dx)=(((x^(6))/(6))^(6))/(((x^(5))/(5))_(0)^(6))=5m`
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 thin rod of length 6 m is lying along the x-axis with its ends at x = 0 and x = 6m . It linear density (mass/length) varies with x as kx^(4) . Find the position of centre of mass of rod in meters.

A thin rod of length L is lying along the x-axis with its ends at x = 0 and x = L. Its linear density (mass/length) varies with x as k((x)/(L))^n where n can be zero or any positive number. If the position X_(CM) of the centre of mass of the rod is plotted against n, which of the following graphs best approximates the dependence of X_(CM) on n?

If the linear density of a rod of length L varies as lambda = A+Bx , find the position of its centre of mass .

If linear density of a rod of length 3m varies as lamda=2+x , then the position of the centre of mass of the rod is P/7m . Find the value of P.

A rod of length L is placed along the x-axis between x=0 and x=L . The linear mass density (mass/length) rho of the rod varies with the distance x from the origin as rho=a+bx . Here, a and b are constants. Find the position of centre of mass of this rod.

If linear density of a rod of length 3m varies as lambda = 2 + x, them the position of the centre of gravity of the rod is

A rod of length L is placed along the x-axis between x = 0 and x = L. The linear density (mass/length) lamda of the rod varies with the distance x from the origin as lamda = Rx. Here, R is a positive constant. Find the position of centre of mass of this rod.

A rod of length L is placed along the x-axis between x = 0 and x = L. The linear density (mass/ length) lambda of the rod varies with the distance x from the origin as lambda = Rx . Here, R is a positive constant. Find the position of centre of mass of this rod.

A rod of length L is placed along the X-axis between x=0 and x=L . The linear density (mass/length) rho of the rod varies with the distance x from the origin as rhoj=a+bx. a. Find the SI units of a and b. b. Find the mass of the rod in terms of a,b, and L.

ALLEN-TEST PAPERS-MATHS
  1. A thin rod of length 6 m is lying along the x-axis with its ends at x=...

    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

    |