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A force F is given by F = at + bt^(2) , ...

A force `F` is given by `F = at + bt^(2)` , where `t` is time . What are the dimensions of `a and b`?

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To find the dimensions of constants \( a \) and \( b \) in the equation \( F = at + bt^2 \), we will follow these steps: ### Step 1: Identify the dimensions of force The dimension of force \( F \) is given by: \[ [F] = M L T^{-2} \] where \( M \) is mass, \( L \) is length, and \( T \) is time. ...
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Knowledge Check

  • A force is given by F = a t + b t^(2) , where, t is the time. What are the dimensions of a and b?

    A
    `[MLT^(-4)] and [MLT]`
    B
    `[MLT^(-1)] and [MLT^(0)]`
    C
    `[MLT^(-3)] and [MLT^(-4)]`
    D
    `[MLT^(-3)] and [MLT^(0)]`

  • A force F is given by F = at + bt^(2) , where t is time. The dimensions of a and b are

    A
    `[MLT^(-3)]` and `[MLT^(-4)]`
    B
    `[MLT^(-4)]` and `[MLT^(-3)]`
    C
    `[MLT^(-1)]` and `[MLT^(-2)]`
    D
    `[MLT^(-2)]` and `[MLT^(0)]`

  • A force F is given by F = at+ bt^(2) , where t is time. The dimensions of a and b are

    A
    `[MLT^(-3)] and [M LT^(-4)]`
    B
    `[M LT(-4)] and [M L T^(-3)]`
    C
    `[ M L T^(-1)] and [MLT^(-2)]`
    D
    `[MLT^(-2)] and [MLT^(0)]`

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