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Q.

As shown in the figure a person is pulling a mass ' m ' from ground on a fixed rough hemispherical surface upto the top of the hemisphere with the help of a light inextensible string. Find the work done (in Joules) by tension in the string on mass m if radius of hemisphere is R and friction coefficient is $μ$ . Assume that the block is pulled with negligible velocity (take $μ$ = 0.2, m = 1kg, g = 10m/s², R = 0.5m).

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Detailed Solution

$μ$ (11)
Sol. Work energy Theorem on “m”
Question Image
W_G + N + W_T + W_f = $∆$ K
$- m g R + O + W_{T} - \int_{0}^{\frac{π}{2}} (μ m g \sin θ) R d θ = 0$
$\Rightarrow$ W_T = mgR ( $μ$ + 1)

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As shown in the figure a person is pulling a mass ' m ' from ground on a fixed rough hemispherical surface upto the top of the hemisphere with the help of a light inextensible string. Find the work done (in Joules) by tension in the string on mass m if radius of hemisphere is R and friction coefficient is μ. Assume that the block is pulled with negligible velocity (take μ= 0.2, m = 1kg, g = 10m/s2, R = 0.5m).