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What are the dimensions of a and b in th...

What are the dimensions of a and b in the relation F = at + b x, whrer F is force and x is distance ?

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

  • Write the dimensions of a//b in the relation P = ( a - t^(2))/( bx) , where P is the pressure , x is the distance , and t is the time .

    A
    `M^(-1) L^(0)T^(-2)`
    B
    `M L^(0)T^(-2)`
    C
    `M L^(0)T^(2)`
    D
    `M LT^(-2)`

  • The quantities A and B are related by the relation A//B = m , where m is the linear mass density and A is the force , the dimensions of B will be

    A
    Same as that of pressure
    B
    Same as that of work
    C
    That of momentum
    D
    Same as that of learnt heat

  • The quantities A and B are related by the relation, m=A//B , where m is the linear density and A is the force. The dimensions of B are of

    A
    pressure
    B
    latent heat
    C
    work
    D
    None of these

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