A heavy solid sphere of mass 15kg and radius 0.2 m is placed on a perfectly rough horizontal surface of a wedge of mass 5kg as shown in the figure. Match the column for the value of physical quantities in SI unit. (Take g = 10 ms–2)List - IList - II(P) Acceleration of wedge(1) 5.2(Q) Acceleration of sphere with respect to the wedge(2) 9.1(R) Angular acceleration of the sphere(3) 31.2(S) Frictional force action on the sphere(4) 26

Engineering

Physics

Moment of Inertia

Rolling

Motion of Block on Horizontal Surface

Constrained Motion

Question

A heavy solid sphere of mass 15kg and radius 0.2 m is placed on a perfectly rough horizontal surface of a wedge of mass 5kg as shown in the figure. Match the column for the value of physical quantities in SI unit. (Take g = 10 ms^–2)

List - I	List - II
(P) Acceleration of wedge	(1) 5.2
(Q) Acceleration of sphere with respect to the wedge	(2) 9.1
(R) Angular acceleration of the sphere	(3) 31.2
(S) Frictional force action on the sphere	(4) 26

P → 2
Q → 1
R → 3
S → 4

P → 2
Q → 1
R → 4
S → 3

P → 4
Q → 1
R → 2
S → 3

P → 3
Q → 1
R → 4
S → 2

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N + 9a = 150 ... (1)
12a – f_s = 15b ... (2)
$f_{s} \times R = \frac{2}{5} \times 15 \times R^{2} \times α$ ... (3)
b = αR ... (4)

(N + 50) sin 37° – f_s cos 37° = 5a ... (5)
solving eq. (i), (ii), (iii), (iv) & (v)
we get a = 9.1 ms^–2, b = 5.2 ms^–2,
a = 26 rad/sec², f_s = 31.2