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NEET 2010
Exam
NEET
Year
2010
Subject
Physics
Chapter
Laws of Motion

NEET 2010 · Physics · Laws of Motion

A block of mass m is in contact with the cart C as shown in the...

A block of mass m\mathrm{m} is in contact with the cart C\mathrm{C} as shown in the figure. A block of mass m is in contact with the cart C as shown in the figure. The coefficient of static friction between the
The coefficient of static friction between the block and the cart is μ\mu. The acceleration α\alpha of the cart that will prevent the block from falling satisfies

Options

  1. Aα>mgμ\alpha>\frac{m g}{\mu}
  2. Bα>gμm\alpha>\frac{g}{\mu \mathrm{m}}
  3. Cα≥gμ\alpha \geq \frac{g}{\mu}
  4. Dα<gμ\alpha < \frac{g}{\mu}

Correct answer

C. α≥gμ\alpha \geq \frac{g}{\mu}

Step-by-step solution

When a cart moves with some acceleration toward right then a pseudo force (ma) acts on block toward left. This force (mα)(m \alpha) is action force by a block on cart Now, block will remain static w.r.t. cart, if frictional force μR≥mg\mu \mathrm{R} \geq \mathrm{mg}⇒μmα≥mg [as R=mα ] ⇒α≥gμ\begin{array}{crrr} \Rightarrow & \mu \mathrm{m} \alpha & \geq \mathrm{mg} & \text{ [as } \mathrm{R}=\mathrm{m} \alpha \text{ ] } \\ \Rightarrow & \alpha & \geq \frac{g}{\mu} & \end{array}
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