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Consider the equation T = 2pi sqrt ((l)/...

Consider the equation `T = 2pi sqrt ((l)/(g))` and check whether it is correct or not.

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To check whether the equation \( T = 2\pi \sqrt{\frac{l}{g}} \) is dimensionally correct, we need to compare the dimensions on both sides of the equation. Here’s the step-by-step solution: ### Step 1: Determine the dimension of the left-hand side (LHS) The LHS of the equation is \( T \), which represents the time period. - The dimension of time \( T \) is \([T]\). ### Step 2: Determine the dimension of the right-hand side (RHS) ...
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The time t of a complete oscillation of a simple pendulum of length l is given by the equation T=2 pi sqrt((1)/(g)) where g is constant.What is the percentage error in T when l is increased by 1%?

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Knowledge Check

  • The equation T=2pisqrt(l//g) is valid only when

    A
    the length of the pendulum is less than the radius the earth
    B
    the length of the pendulum is greater than or equal to radius by the earth
    C
    the length of pendulum is independent of the radius of the earth
    D
    length of the pendulum is equal to radius and the earth.

  • A small metallic bob of mass m of a simple pendulum of length l is suspended from a silk threas between two parallel charged plates.The electric field intensity E act vertically downwards . If bob is given a charge + q ,time period of oscillation (i) T = 2 pi sqrt((l)/((g - (qE)/(m)))) , if the lower plate is charged positively (ii) T = 2 pi sqrt((l)/((g - (qE)/(m)))) ,if the lower plate is charged negatively (iii) T = 2 pi sqrt((l)/((g + (qE)/(m)))) ,if the lower plate is charged positively (iv) T = 2 pi sqrt((l)/((g + (qE)/(m)))) , if the lower plate is charged negatively

    A
    `(i) ,(ii)`
    B
    `(i),(iii)`
    C
    `(i),(iv)`
    D
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