(C) Let $m_b = 50 \; g = 0.05 \; kg$ be the mass of the bob and $m_u = 75 \; g = 0.075 \; kg$ be the mass of the bullet. The length of the pendulum is

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(C) Let $m_b = 50 \; g = 0.05 \; kg$ be the mass of the bob and $m_u = 75 \; g = 0.075 \; kg$ be the mass of the bullet. The length of the pendulum is $R = 2 \; m$.For the bob to just complete a vertical circle,the minimum velocity $u$ at the lowest point must be $u = \sqrt{5gR}$.Substituting the values: $u = \sqrt{5 \times 10 \times 2} = \sqrt{100} = 10 \; m/s$.By the principle of conservation of linear momentum in the horizontal direction during the collision:$m_u v = m_u (v/3) + m_b u$$0.075 v = 0.075 (v/3) + 0.05 (10)$$0.075 v - 0.025 v = 0.5$$0.05 v = 0.5$$v = 10 \; m/s$.

Class 11 Physics Work, Energy and Power Mix Examples-Work, Energy, Power and Collision

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$A$ pendulum of length $2 \; m$ consists of a wooden bob of mass $50 \; g$. $A$ bullet of mass $75 \; g$ is fired towards the stationary bob with a speed $v$. The bullet emerges out of the bob with a speed $\frac{v}{3}$ and the bob just completes the vertical circle. The value of $v$ is $\dots \; ms^{-1}$. (if $g = 10 \; m/s^2$)

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Mix Examples-Work, Energy, Power and Collision

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$A$ body is moved from rest along a straight line by a machine delivering constant power. The ratio of displacement and velocity $(s/v)$ varies with time $t$ as :

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$A$ force of $10 \ N$ acting at an angle on a particle produces a displacement of $(3 \hat{i} - 4 \hat{\jmath}) \ m$. Due to this force,if the kinetic energy of the particle is decreased by $25 \ J$,then the angle between the force and the displacement is:

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State whether the following statements are true or false:
$(a)$ Power is the vector product of force and velocity.
$(b)$ $1\,kg\,m = 9.8\,J$
$(c)$ When a teacher rubs a blackboard with a duster,they do no work.
$(d)$ Kinetic energy can be negative.