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If force F=(2x+3x^(2))N is applied on a ...

If force `F=(2x+3x^(2))N` is applied on a particle along x = axis, then find the work done by it during motion of particle from x = 0 to x = 2 m.

Text Solution

AI Generated Solution

To find the work done by the force \( F = (2x + 3x^2) \, \text{N} \) on a particle as it moves from \( x = 0 \) to \( x = 2 \, \text{m} \), we can follow these steps: ### Step 1: Understand the Work Done Formula The work done \( W \) by a force when it moves an object along a path can be calculated using the formula: \[ W = \int_{x_1}^{x_2} F \, dx \] where \( F \) is the force applied, and \( dx \) is the infinitesimal displacement. ...
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Knowledge Check

  • A force F=-k/x_2(x!=0) acts on a particle in x-direction. Find the work done by this force in displacing the particle from. x = + a to x = 2a . Here, k is a positive constant.

    A
    `-k/2a`
    B
    `-k/a`
    C
    `-2k/a`
    D
    `-a/k`
  • A force F = (2+ x)N acts on a particle in the x-direction. The work done by this force during a displacement from x = 1.0 m to x = 2.0 m is

    A
    `2.1 J`
    B
    `2.5 J`
    C
    `3.5 J`
    D
    `4.5 J`
  • A force F=Kx^(2) acts on a particle at an angle of 60° with the x–axis. the work done in displacing the particle from x_(1) to x_(2) will be –

    A
    `(kx^(2))/(2)`
    B
    `(k)/(2)(x_(2)^(2)-x_(1)^(2))`
    C
    `(k)/(6)(x_(2)^(3)-x_(1)^(3))`
    D
    `(k)/(3)(x_(2)^(3)-x_(1)^(3))`
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