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(D) For the coin to revolve with the record without slipping,the required centripetal force must be provided by the static frictional force.The centri

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$r \le \frac{\mu g}{\omega^2}$

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(D) For the coin to revolve with the record without slipping,the required centripetal force must be provided by the static frictional force.The centripetal force required for circular motion is $F_c = m \omega^2 r$.The maximum static frictional force available is $f_{s, 	ext{max}} = \mu N = \mu m g$.For the coin to stay in place,the static friction must be greater than or equal to the required centripetal force:$f_{s, 	ext{max}} \ge F_c$Substituting the expressions:$\mu m g \ge m \omega^2 r$Dividing both sides by $m \omega^2$ (assuming $m$ and $\omega$ are non-zero):$r \le \frac{\mu g}{\omega^2}$

Column-$I$	Column-$II$
$(a)$ Parturition	$(p)$ Attachment of embryo to endometrium
$(b)$ Gestation	$(q)$ Release of egg from Graafian follicle
$(c)$ Ovulation	$(r)$ Delivery of Foetus from uterus
$(d)$ Implantation	$(s)$ Duration between pregnancy and birth
	$(t)$ Formation of zygote by fusion of egg and sperm

$A$ gramophone record is revolving with an angular velocity $\omega$. $A$ coin is placed at a distance $r$ from the centre of the record. The static coefficient of friction is $\mu$. The coin will revolve with the record if

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