Q. Three equal weights of mass $3 kg$ each are hanging on a string passing over a fixed pulley as shown in figure-$2.147.$ The tension in the string connecting weight $B$ and $C$ is : (Take $g=10 \,m / s ^{2}$ )

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A

$1\, kg \,w t$

B

$2 \,kg \,w t$

C

$3\, kg \,w t$

D

$4 \,kg \,wt$

Solution:

For $A, T_{1}-30 =3 a \,\,\,$...(1)
$ \Rightarrow T_{1} =30+3 a
For $B, 30+T_{2}-T_{1} =3 a\,\,\.$...(2)

From $(1),(2)$ and (3),
$30+30-3 a-30-3 a=3 a$
$9 a=30$
$a=\frac{10}{3} \,m / s ^{2}$
$T_{2}=30-3\left(\frac{10}{3}\right)$
$T_{2}=20 \,N =2 \,kgwt$

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Q. Three equal weights of mass $3 kg$ each are hanging on a string passing over a fixed pulley as shown in figure-$2.147.$ The tension in the string connecting weight $B$ and $C$ is : (Take $g=10 \,m / s ^{2}$ )

$1\, kg \,w t$

$2 \,kg \,w t$

$3\, kg \,w t$

$4 \,kg \,wt$

For $A, T_{1}-30 =3 a \,\,\,$...(1) $ \Rightarrow T_{1} =30+3 a For $B, 30+T_{2}-T_{1} =3 a\,\,\.$...(2) From $(1),(2)$ and (3), $30+30-3 a-30-3 a=3 a$ $9 a=30$ $a=\frac{10}{3} \,m / s ^{2}$ $T_{2}=30-3\left(\frac{10}{3}\right)$ $T_{2}=20 \,N =2 \,kgwt$

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1. In the following figure, an object of mass $ 1.2\, kg $ is at rest at point $ P $ . lf $ R $ and $ F $ are the reaction and the frictional force, respectively, then

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3. Three blocks are connected, as shown in the figure. Calculate the minimum force required to move the blocks with constant velocity. The co-efficient of friction at all surfaces is $0.25$ . [Assume that rod does not exerts force in vertical direction]

4. A car is moving with speed $20 \, \, \text{m s}^{- 1}$ on a circular path of radius $100 \, \, \text{m}$ . Its speed is increasing at a rate of $3 \, \text{m s}^{- 2}$ . The magnitude of the acceleration of the car at that moment is

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For $A, T_{1}-30 =3 a \,\,\,$...(1)
$ \Rightarrow T_{1} =30+3 a
For $B, 30+T_{2}-T_{1} =3 a\,\,\.$...(2)

From $(1),(2)$ and (3),
$30+30-3 a-30-3 a=3 a$
$9 a=30$
$a=\frac{10}{3} \,m / s ^{2}$
$T_{2}=30-3\left(\frac{10}{3}\right)$
$T_{2}=20 \,N =2 \,kgwt$

3. Three blocks are connected, as shown in the figure. Calculate the minimum force required to move the blocks with constant velocity. The co-efficient of friction at all surfaces is $0.25$ .

[Assume that rod does not exerts force in vertical direction]