KCET · Physics · Rotational Motion

Two fly wheels are connected by a non-slipping belt as shown in the figure. \(I_1=4 \mathrm{~kg} \mathrm{~m}^2, r_1=20 \mathrm{~cm}\), \(\mathrm{I}_2=20 \mathrm{kgm}^2\) and \(\mathrm{r}_2=30 \mathrm{~cm}\). A torque of 10 Nm is applied on the smaller wheel. Then match the entries of column I with appropriate entries of column II.
Quantities Their numerical Values (in SI units)
a. Angular acceleration of smaller wheel 1. \(\frac{5}{3}\)
b. Torque on the larger wheel 2. \(\frac{100}{3}\)
c. Angular acceleration of larger wheel 3. \(\frac{5}{2}\)

A a - ii, b-iii, c - i
B a-iii, b-i, c-ii
C a-ii, b-i, c-iii
D a - iii, b-ii, c-i

Verified Solution

Answer & Solution

Correct Answer

(D) a - iii, b-ii, c-i

Step-by-step Solution

Detailed explanation

\(\begin{array}{ll}\mathrm{T}_1=\mathrm{I}_1 \alpha_1 & \alpha_2 \mathrm{H}_2=\alpha_1 \mathrm{H}_1 \\ 10=\alpha_1 \times 4 & \alpha_2 \times 0.3=\frac{5}{2} \times 0.2 \\ \therefore \alpha_1=\frac{5}{2} \mathrm{SI} & \alpha_2=\frac{5}{3} \mathrm{SI} \\ \therefore \mathrm{T}_2=\mathrm{I}_2 \alpha_2=20 \times \frac{5}{3}=\frac{100}{3} \mathrm{SI}\end{array}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match the following Maxwell's equations:
(The symbols used here have their usual meanings)

List-I		List-II
(a)	Gauss' law for electrostatics	(i)	\(\oint \vec{E} \cdot d\vec{A} = \dfrac{Q}{\varepsilon_0}\)
(b)	Gauss' law for magnetism	(ii)	\(\oint \vec{B} \cdot d\vec{l} = \mu_0 \left[i_c + \varepsilon_0 \dfrac{d\phi_E}{dt}\right]\)
(c)	Faraday's law	(iii)	\(\oint \vec{B} \cdot d\vec{A} = 0\)
(d)	Ampere-Maxwell's law	(iv)	\(\oint \vec{E} \cdot d\vec{l} = -\dfrac{d\phi_B}{dt}\)

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Quantities	Their numerical Values (in SI units)
a. Angular acceleration of smaller wheel	1. \(\frac{5}{3}\)
b. Torque on the larger wheel	2. \(\frac{100}{3}\)
c. Angular acceleration of larger wheel	3. \(\frac{5}{2}\)