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Applying NLM along 3 Axis

Three blocks ...

Question

Three blocks $P, Q$ and $R$ of masses $5 k g, 4 k g$ respectively are connected by a light inextensibile string and they are moved on a smooth horizontal plane. If a force of $24 N$ is applied to the string connected to $R$ , tensions $T_{1}$ and $T_{2}$ in the string are:

20 N, 5 N

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5 N, 20 N

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10 N, 18 N

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18 N, 10 N

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Solution

The correct option is D $18 N, 10 N$
Given that,

Force $F = 24 N$

Mass of $P = 5 k g$

Mass of $Q = 4 k g$

Mass of $R = 3 k g$

Now, the acceleration is

$F = m a$

$24 = (5 + 4 + 3) a$

$a = \frac{24}{12}$

$a = 2 m / s^{2}$

According to FBD
Now, the tension is

$24 - T_{1} = 3 a$

$24 - T_{1} = 6$

$T_{1} = 18 N$

Now, again

$T_{1} - T_{2} = 4 a$

$18 - T_{2} = 8$

$T_{2} = 10 N$

Hence, the tension is $T_{1} = 18 N$ and $T_{2} = 10 N$

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Three blocks P,Q and R of masses 5 kg,4 kg respectively are connected by a light inextensibile string and they are moved on a smooth horizontal plane. If a force of 24 N is applied to the string connected to R, tensions T1 and T2 in the string are:

The correct option is D 18 N,10 NGiven that, Force F=24N Mass of P=5kg Mass of Q=4kg Mass of R=3kg Now, the acceleration is F=ma 24=(5+4+3)a a=2412 a=2m/s2 According to FBDNow, the tension is 24−T1=3a 24−T1=6 T1=18N Now, again T1−T2=4a 18−T2=8 T2=10N Hence, the tension is T1=18N and T2=10N

Three blocks $P, Q$ and $R$ of masses $5 k g, 4 k g$ respectively are connected by a light inextensibile string and they are moved on a smooth horizontal plane. If a force of $24 N$ is applied to the string connected to $R$ , tensions $T_{1}$ and $T_{2}$ in the string are: