Question Number 20040 by Tinkutara last updated on 20/Aug/17
$$\mathrm{The}\:\mathrm{system}\:\mathrm{shown}\:\mathrm{in}\:\mathrm{figure}\:\mathrm{is}\:\mathrm{given}\:\mathrm{an} \\ $$$$\mathrm{acceleration}\:'{a}'\:\mathrm{toward}\:\mathrm{left}.\:\mathrm{Assuming} \\ $$$$\mathrm{all}\:\mathrm{the}\:\mathrm{surfaces}\:\mathrm{to}\:\mathrm{be}\:\mathrm{frictionless},\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{force}\:\mathrm{on}\:\mathrm{the}\:\mathrm{sphere}\:\mathrm{by}\:\mathrm{inclined} \\ $$$$\mathrm{surface}. \\ $$
Commented by Tinkutara last updated on 20/Aug/17
Commented by ajfour last updated on 21/Aug/17
$${let}\:{force}\:{on}\:{sphere}\:{by}\:{incline}\: \\ $$$${be}\:{N}\:. \\ $$$$\Sigma{F}_{{y}} =\mathrm{0}\:\:,\:{so}\:\:{N}\mathrm{cos}\:\mathrm{30}°\:={mg} \\ $$$$\Rightarrow\:\:\:{N}=\frac{\mathrm{2}{mg}}{\sqrt{\mathrm{3}}}\:. \\ $$
Commented by Tinkutara last updated on 21/Aug/17
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{very}\:\mathrm{much}\:\mathrm{Sir}! \\ $$