(A) Since the surface of the bowl is smooth,there is no friction to cause the sphere to roll. The sphere will simply slide down the surface.By the law

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(A) Since the surface of the bowl is smooth,there is no friction to cause the sphere to roll. The sphere will simply slide down the surface.By the law of conservation of mechanical energy,the loss in potential energy is equal to the gain in kinetic energy.The change in height of the center of mass of the sphere is $h = R - r$.Potential energy lost = $mgh = mg(R - r)$.Since the sphere is sliding (not rolling),its total kinetic energy is purely translational: $K = \frac{1}{2} mv^2$.Therefore,the total kinetic energy at the lowest point is $K = mg(R - r)$.

Class 11 Physics Work, Energy, Power and Collision Work Energy Theorem and Conservation of Mechanical Energy

Easy

$A$ small sphere of mass $m$ and radius $r$ slides down the smooth surface of a large hemispherical bowl of radius $R$. If the sphere starts sliding from rest,the total kinetic energy of the sphere at the lowest point $A$ of the bowl will be [given,moment of inertia of sphere $= \frac{2}{5} mr^2$].

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A
$mg(R-r)$
B
$\frac{7}{10} mg(R-r)$
C
$\frac{2}{7} mg(R-r)$
D
$\frac{10}{7} mg(R-r)$

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Work, Energy, Power and Collision

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Work Energy Theorem and Conservation of Mechanical Energy

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$A$ small sphere of mass $m$ and radius $r$ slides down the smooth surface of a large hemispherical bowl of radius $R$. If the sphere starts sliding from rest,the total kinetic energy of the sphere at the lowest point $A$ of the bowl will be [given,moment of inertia of sphere $= \frac{2}{5} mr^2$].

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Explain the conservation of mechanical energy using the example of a falling ball.

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$A$ body of mass $2 \, kg$ is projected vertically upwards with a velocity of $2 \, m/s$. The kinetic energy $(K.E.)$ of the body just before striking the ground is ............. $J$.

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