A sphere of mass m makes SHM in a hemispherical bowl ABC . It moves from A to C , and then back to A via ABC . It is considered that PB=h . If acceleration due to gravity be g then the speed of the ball when it just crosses the point B will be,

Question

A sphere of mass m makes SHM in a hemispherical bowl ABC . It moves from A to C , and then back to A via ABC . It is considered that PB=h . If acceleration due to gravity be g then the speed of the ball when it just crosses the point B will be, <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-k2lpo11xnr4rdakn.jpg" /> (A) 2gh (B) mgh (C) √2 g h (D) (g h/2)

Tardigrade Admin · Accepted Answer

Potential energy at A is converted into K.E. at B ∴ mgh=(1/2)mvB2=2gh,vB=√2 g h

Q. A sphere of mass $m$ makes SHM in a hemispherical bowl $A BC$ . It moves from $A$ to $C$ , and then back to $A$ via $A BC$ . It is considered that $PB = h$ . If acceleration due to gravity be $g$ then the speed of the ball when it just crosses the point $B$ will be,

$2 g h$

$m g h$

$2 g h$

$\frac{g h}{2}$

Potential energy at $A$ is converted into K.E. at $B$
$∴ m g h = \frac{1}{2} m v_{B}^{2} = 2 g h, v_{B} = 2 g h$

Q. A sphere of mass m makes SHM in a hemispherical bowl ABC . It moves from A to C , and then back to A via ABC . It is considered that PB=h . If acceleration due to gravity be g then the speed of the ball when it just crosses the point B will be,

2gh

mgh

2gh​

2gh​

Potential energy at A is converted into K.E. at B ∴mgh=21​mvB2​=2gh,vB​=2gh​

Q. A sphere of mass $m$ makes SHM in a hemispherical bowl $A BC$ . It moves from $A$ to $C$ , and then back to $A$ via $A BC$ . It is considered that $PB = h$ . If acceleration due to gravity be $g$ then the speed of the ball when it just crosses the point $B$ will be,

$2 g h$

$m g h$

$2 g h$

$\frac{g h}{2}$

Potential energy at $A$ is converted into K.E. at $B$
$∴ m g h = \frac{1}{2} m v_{B}^{2} = 2 g h, v_{B} = 2 g h$