In the given figure. List - I List - II (P) If F = 50 N , θ = 5 3 ∘ and μ = 6 1 then acceleration of block is (1) 3 i ^ (Q) If F = 100 N , θ = 3 7 ∘ and μ = 1.5 then acceleration of block is (2) 2 i

Question

In the given figure. List - I List - II (P) If F = 50 N , θ = 5 3 ∘ and μ = 6 1 ​ then acceleration of block is (1) 3 i ^ (Q) If F = 100 N , θ = 3 7 ∘ and μ = 1.5 then acceleration of block is (2) 2 i ^ (R) If F = 200 N , θ = 5 3 ∘ and μ = 1.0 then acceleration of block is (3) 12 i ^ + 6 j ^ ​ (S) If F = 110 N , θ = 9 0 ∘ and μ = 0.2 then acceleration of block is (4) 1 j ^ ​ (5) 12 i ^ + 16 j ^ ​

TestHub · Accepted Answer

Mass of block m = 10 kg, g = 10 m/s², so mg = 100 N.

If F sinθ < mg: N = mg - F sinθ, friction f = μN, and $a = \frac{F c o s θ - f}{m} \hat{i}$

If F sinθ > mg: the block leaves the surface (N = 0, f = 0) and $a = \frac{F c o s θ}{m} \hat{i} + \frac{F s i n θ - m g}{m} \hat{j}$

(P) F = 50 N, θ = 53°: F sinθ = 40 < 100; N = 60, f = (1/6)×60 = 10; $a = \frac{50 c o s 5 3 ^{\circ} - 10}{10} = \frac{30 - 10}{10} = 2 \hat{i} \to (2)$

(Q) F = 100 N, θ = 37°: F sinθ = 60; N = 40, f = 1.5×40 = 60; $a = \frac{100 c o s 3 7 ^{\circ} - 60}{10} = \frac{80 - 60}{10} = 2 \hat{i} \to (2)$

(R) F = 200 N, θ = 53°: F sinθ = 160 > 100, block lifts off; $a = \frac{200 c o s 5 3 ^{\circ}}{10} \hat{i} + \frac{160 - 100}{10} \hat{j} = 12 \hat{i} + 6 \hat{j} \to (3)$

(S) F = 110 N, θ = 90°: F sinθ = 110 > 100, block lifts off; $a = \frac{110 - 100}{10} \hat{j} = 1 \hat{j} \to (4)$

Hence P→2, Q→2, R→3, S→4, option (C).

List - I	List - II
(P) If $F = 50 N, θ = 5 3^{\circ}$ and $μ = \frac{1}{6}$ then acceleration of block is	(1) $3 \hat{i}$
(Q) If $F = 100 N, θ = 3 7^{\circ}$ and $μ = 1.5$ then acceleration of block is	(2) $2 \hat{i}$
(R) If $F = 200 N, θ = 5 3^{\circ}$ and $μ = 1.0$ then acceleration of block is	(3) $12 \hat{i} + 6 \hat{j}$
(S) If $F = 110 N, θ = 9 0^{\circ}$ and $μ = 0.2$ then acceleration of block is	(4) $1 \hat{j}$
	(5) $12 \hat{i} + 16 \hat{j}$

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