A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then, [2009]

Question

Smart Achievers · Accepted Answer

(2, 3)

Here, ${\vec{V}}_{A} = 0$

${\vec{V}}_{B} = {\vec{V}}_{0}$

${\vec{V}}_{C} = 2 {\vec{V}}_{0}$

$∴$ ${\vec{V}}_{C} - {\vec{V}}_{B} = {\vec{V}}_{B} - {\vec{V}}_{A}$

$and$ $| {\vec{V}}_{C} - {\vec{V}}_{A} |$ $=$ $| {\vec{V}}_{B} - {\vec{V}}_{C} |$

Solution

Q.
A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then, [2009]

1 ${\vec{V}}_{C} - {\vec{V}}_{A} = 2 ({\vec{V}}_{B} - {\vec{V}}_{C})$

2 ${\vec{V}}_{C} - {\vec{V}}_{B} = {\vec{V}}_{B} - {\vec{V}}_{A}$

3 $| {\vec{V}}_{C} - {\vec{V}}_{A} |$ $= 2$ $| {\vec{V}}_{B} - {\vec{V}}_{C} |$

4 $| {\vec{V}}_{C} - {\vec{V}}_{A} |$ $= 4$ $| {\vec{V}}_{B} |$

Ans.
(2, 3)

Here, ${\vec{V}}_{A} = 0$

${\vec{V}}_{B} = {\vec{V}}_{0}$

${\vec{V}}_{C} = 2 {\vec{V}}_{0}$

$∴$ ${\vec{V}}_{C} - {\vec{V}}_{B} = {\vec{V}}_{B} - {\vec{V}}_{A}$

$and$ $| {\vec{V}}_{C} - {\vec{V}}_{A} |$ $=$ $| {\vec{V}}_{B} - {\vec{V}}_{C} |$

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Solution

Q. A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure, A is the point of contact, B is the centre of the sphere and C is its topmost point. Then, [2009]

1 V→C-V→A=2(V→B-V→C)

2 V→C-V→B=V→B-V→A

3 |V→C-V→A|=2|V→B-V→C|

4 |V→C-V→A|=4|V→B|

Ans. (2, 3) Here, V→A=0 V→B=V→0 V→C=2V→0 ∴ V→C-V→B=V→B-V→A and |V→C-V→A|=|V→B-V→C|