A cylinder, hollow sphere, solid sphere and a ring all having mass 1 kg are released from rest on a inclined plane having angle of inclination 37° (tan 37° = 3/4). Coefficient of friction between bodies and plane is 'µ', then match the following column .
Column I | Column II |
(i) If µ < 0.25 body which must not undergo pure rolling motion | [A] Ring |
(ii) If µ 0.3 work done by friction must be negative for | [B] Hollow sphere |
(iii) If µ = 0.4, total mechanical energy will be conserved for | [C] Solid sphere |
(iv) If µ = 0.25, friction force will be 2N for | [D] Cylinder |
Text Solution
Verified by ExpertsA
The gravitational force acting parallel to the plane, which causes acceleration, is given by:
$$F = mg \sin \theta$$
where $$m = 1 \text{ kg}$$ and $$\theta = 37^\circ$$. For all objects, the mass, m = 1 kg. Thus, $$F = 1 \cdot g \cdot \sin(37^\circ) = 1 \cdot 9.81 \cdot \frac{3}{5} = 5.88\text{ N}$$ (approximating g as 9.81 m/s²).
Step 2: Determine the frictional force, which can be expressed as
$$F_f = \mu N$$
where N is the normal force given by:
$$N = mg \cos \theta = 1 \cdot 9.81 \cdot \frac{4}{5} = 7.848\text{ N}$$. Hence,
$$F_f = \mu \cdot 7.848\
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