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Current Question (ID: 9775)
Question:
$\text{A block } B \text{ is placed on top of block } A. \text{ The mass of block } B \text{ is less than the mass of block } A. \text{ Friction exists between the blocks, whereas the ground on which block } A \text{ is placed is assumed to be smooth. A horizontal force } F, \text{ increasing linearly with time begins to act on } B. \text{ The acceleration } a_A \text{ and } a_B \text{ of blocks } A \text{ and } B \text{ respectively are plotted against } t. \text{ The correctly plotted graph is:}$
Options:
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1. $\text{Graph 1: } a_B \text{ starts above } a_A \text{ and both increase linearly with } a_B > a_A$
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2. $\text{Graph 2: } a_B \text{ and } a_A \text{ both start from origin and increase linearly with } a_B > a_A$
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3. $\text{Graph 3: } a_B \text{ starts below } a_A \text{ and both increase with } a_B < a_A \text{ initially}$
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4. $\text{Graph 4: } a_B \text{ and } a_A \text{ both start from origin, } a_A \text{ remains constant while } a_B \text{ increases}$
Solution:
\text{Analysis of the problem:}
\text{Initially, when the applied force is less than limiting friction between block A and B, the whole system moves with common acceleration:}
a_A = a_B = \frac{F}{m_A + m_B}
\text{But as the applied force increases with time, block B starts moving under the effect of net force } F - F_k
\text{Where } F_k = \text{kinetic friction between block A and B}
\text{Acceleration of block B: } a_B = \frac{F - F_k}{m_B}
\text{As F is increasing with time, so } a_B \text{ will increase with time}
\text{Kinetic friction is the cause of motion of block A}
\text{Acceleration of block A: } a_A = \frac{F_k}{m_A}
\text{It is clear that } a_B > a_A \text{, i.e. graph (4) correctly represents the variation in acceleration with time for block A and B.}
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