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Question Number 20724 by Tinkutara last updated on 01/Sep/17

$$\mathrm{A}\mathrm{sphere}\mathrm{is}\mathrm{rolling}\mathrm{without}\mathrm{slipping}\mathrm{on}$$$$\mathrm{a}\mathrm{fixed}\mathrm{horizontal}\mathrm{plane}\mathrm{surface}.\mathrm{In}\mathrm{the}$$$$\mathrm{Figure},\mathrm{A}\mathrm{is}\mathrm{a}\mathrm{point}\mathrm{of}\mathrm{contact},B\mathrm{is}\mathrm{the}$$$$\mathrm{centre}\mathrm{of}\mathrm{the}\mathrm{sphere}\mathrm{and}C\mathrm{is}\mathrm{its}\mathrm{topmost}$$$$\mathrm{point}.\mathrm{Then}$$$$\left(a\right){\overrightarrow{v}}_{\mathrm{C}}-{\overrightarrow{v}}_{\mathrm{A}}=2({\overrightarrow{v}}_{\mathrm{B}}-{\overrightarrow{v}}_{\mathrm{C}})$$$$\left(b\right){\overrightarrow{v}}_{\mathrm{C}}-{\overrightarrow{v}}_{\mathrm{B}}={\overrightarrow{v}}_{\mathrm{B}}-{\overrightarrow{v}}_{\mathrm{A}}$$$$\left(c\right)\mid {\overrightarrow{v}}_{\mathrm{C}}-{\overrightarrow{v}}_{\mathrm{A}}\mid =2\mid {\overrightarrow{v}}_{\mathrm{B}}-{\overrightarrow{v}}_{\mathrm{C}}\mid$$$$\left(d\right)\mid {\overrightarrow{v}}_{\mathrm{C}}-{\overrightarrow{v}}_{\mathrm{A}}\mid =4\mid {\overrightarrow{v}}_{\mathrm{B}}\mid$$

Commented by Tinkutara last updated on 01/Sep/17

Commented by ajfour last updated on 01/Sep/17

$$\left(b\right)and\left(c\right)$$$$because\overrightarrow{v_C}=2\overrightarrow{v_B}$$$$and\overrightarrow{v_A}=0.$$

Commented by Tinkutara last updated on 02/Sep/17

$$\mathrm{Thank}\mathrm{you}\mathrm{very}\mathrm{much}\mathrm{Sir}!$$

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