Question

Pulley - massless, frictionless String - massless Wedge-frictionless In the figure find the acceleration of the blocks if the wedge is fixed.

• A. rightwards
• B. rightwards
• C. leftwards
• D. none of these

Answer 1

The correct option is C

leftwards

lets choose that the blocks will move right.

So 5kg block will accelerate down the incline 10kg the incline. String is inextensible, so both will have same acceleration

mg sin$\theta$

T - 10 $\times$ 10 $\times$ $\frac{1}{2}$ = 10a

T - 50 = 10a -------------------(i)

5g sin 45 - T = 5a

$50\left(\frac{1}{\sqrt{2}}\right)-T=5a$ ----------------(ii)

solving (i) & (ii)

We get

$a=\frac{10}{3}\left(\frac{1-\sqrt{2}}{\sqrt{2}}\right)$

Well this is negative $(\because \sqrt{2}>1)$.So math is telling us that the blocks will accelerate in the negative.

direction or the opposite of the chosen direction

Well let's check out how correct all the mathematics behind it is.

Let's change the direction of chosen acceleration.

50 - T = 10a ----------------(iii)

T = $\frac{50}{\sqrt{2}}=5a$ ----------------(iv)

Solving (iii) & (iv) we get

$a=\frac{10}{3}\left(\frac{\sqrt{2}-1}{\sqrt{2}}\right)$

maths checks out

Nice!!!