First slide

Application of Newtons laws

Question

Figure shows two blocks, each of mass m. The system is released from rest. If accelerations of blocks
A and B at any instant (not initially) are a₁ and a₂, respectively, then
.

Moderate

A

$a_{1} = a_{2} \cos θ$
B

$a_{2} = a_{1} \cos θ$
C

$a_{1} = a_{2}$
D

None of these

Solution

Let at any time, their velocities are v₁ and v₂, respectively.
Then $v_{1} = v_{2} \cos θ$
Differentiating: $a_{1} = a_{2} \cos θ - v_{2} \sin θ \frac{d θ}{d t}$
Hence, none of them is correct.
[Note: Option (a) is correct initially, because initially v₂=0]

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