Question

Find the acceleration of the block of mass 2m as shown in the figure. (Strings are massless and inextensible)

- 2g3
- g3
- g4
- g5

Solution

The correct option is **B** g3

From constrained condition and using method of intercept we have,

..L1+..L2+..L3=0

⇒−a1+a2+a2=0⇒a1=2a2……(1)

From FBD of masses m and 2m we have force equations as

T=ma1...........(i)

2mg−2T=2ma2............(ii)

From eq (1), we get

Tm=2[g−Tm]

3Tm=2g⇒T=2mg3

∴ a2=[g−Tm]=[g−2g3]

⇒a2=g3

Thus, the acceleration of 2m mass is g3

From constrained condition and using method of intercept we have,

..L1+..L2+..L3=0

⇒−a1+a2+a2=0⇒a1=2a2……(1)

From FBD of masses m and 2m we have force equations as

T=ma1...........(i)

2mg−2T=2ma2............(ii)

From eq (1), we get

Tm=2[g−Tm]

3Tm=2g⇒T=2mg3

∴ a2=[g−Tm]=[g−2g3]

⇒a2=g3

Thus, the acceleration of 2m mass is g3

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