In a playground,there is a merry-go-round of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The moment of inertia of the merry-go-round is $I = Mk^2 = 120 \ kg 	imes (3 \ m)^2 = 120 	imes 9 = 1080 \ kg \cdot m^2$. Since the child jumps

Vedclass · Accepted Answer

$0.4$

Vedclass · Answer

(C) The moment of inertia of the merry-go-round is $I = Mk^2 = 120 \ kg 	imes (3 \ m)^2 = 120 	imes 9 = 1080 \ kg \cdot m^2$. Since the child jumps tangentially,the initial angular momentum of the system is provided by the child: $L = mvr = 30 \ kg 	imes 5 \ m/s 	imes 4 \ m = 600 \ kg \cdot m^2/s$. The final moment of inertia of the system (merry-go-round + child) is $I_{total} = I + mr^2 = 1080 + 30 	imes (4)^2 = 1080 + 30 	imes 16 = 1080 + 480 = 1560 \ kg \cdot m^2$. By the law of conservation of angular momentum,$L_{initial} = L_{final} \implies 600 = I_{total} \omega$. Therefore,$\omega = \frac{600}{1560} = \frac{60}{156} = \frac{10}{26} \approx 0.3846 \ rad/s$. Rounding to the nearest provided option,the value is $0.4 \ rad/s$.

Similar Questions

The first line in the Lyman series has wavelength $\lambda$. The wavelength of the first line in the Balmer series is

Molar heat capacity $(C_p)$ of water at constant pressure is $75 \ J \ K^{-1} \ mol^{-1}$. The increase in temperature (in $K$) of $100 \ g$ of water when $1 \ kJ$ of heat is supplied to it is

$A$ constant voltage of $25 ~V$ is applied to a series $L-R$ circuit at $t=0$,by closing a switch. What is the potential difference across the resistor and the inductor at time $t=0$?

$A$ conducting rod of length $2l$ is rotating with constant angular speed $\omega$ about its perpendicular bisector. $A$ uniform magnetic field $\vec B$ exists parallel to the axis of rotation. The $e.m.f.$ induced between two ends of the rod is

Vedclass Test Series

Exam Paper Generator

Online Exam Module