12th grade physics explainer video target for NEET 2026 in indian medical entrance exam ---**Question Number:** 40
**Question Stem:**
A horizontal force $f_1$ and a force $f_2$ inclined at $\phi$ with vertical act upon a block of mass $m$ lying on a rough horizontal plane. For equilibrium of the block, coefficient of friction $\mu$ between the block and the surface is
**Options:**
(a) $\frac{(f_1 + f_2 \sin\phi)}{(mg + f_2 \cos\phi)}$
(b) $\frac{(f_1 + f_2 \cos\phi)}{(mg + f_2 \sin\phi)}$
(c) $\frac{(f_1 - f_2 \sin\phi)}{mg - f_2 \cos\phi}$
(d) $\frac{f_1 - f_2 \cos\phi}{mg - f_2 \sin\phi}$
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Let's solve this NEET physics problem step by step. We have a block of mass m on a rough horizontal surface. Two forces act on it: a horizontal force f1 and an inclined force f2 making angle phi with the vertical. For equilibrium, we need to find the coefficient of friction mu.
Now let's resolve the inclined force f2 into its components. Since f2 makes angle phi with the vertical, its horizontal component is f2 sine phi acting rightward, and its vertical component is f2 cosine phi acting downward. For equilibrium, we apply Newton's first law. In the vertical direction, the normal force N balances the weight mg plus the vertical component of f2. In the horizontal direction, the friction force must balance f1 plus the horizontal component of f2.
Now let's write the equilibrium equations. For vertical equilibrium, the upward normal force N must balance the downward forces: the weight mg and the vertical component f2 cosine phi. This gives us N equals mg plus f2 cosine phi. For horizontal equilibrium, the leftward friction force must balance the rightward forces: f1 and the horizontal component f2 sine phi. Therefore, the friction force equals f1 plus f2 sine phi.
For the block to be in limiting equilibrium, the friction force must equal mu times the normal force. Substituting our expressions, we get f1 plus f2 sine phi equals mu times the quantity mg plus f2 cosine phi. Solving for the coefficient of friction mu, we divide both sides to get mu equals f1 plus f2 sine phi divided by mg plus f2 cosine phi. This matches option A in our multiple choice question.
Perfect! We have successfully solved this NEET physics problem. The coefficient of friction mu equals f1 plus f2 sine phi divided by mg plus f2 cosine phi. This matches exactly with option A. Remember the key steps: resolve forces into components, apply equilibrium conditions, and use the friction relationship. This type of problem is common in NEET and tests your understanding of force equilibrium and friction. Good luck with your NEET 2026 preparation!