Applications of Newton's Laws of Motion in Different Frames

Q 1 :
A light stretchable string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ . If the acceleration of the system is $\frac{g}{8}$ , then the ratio of the masses $\frac{m_{2}}{m_{1}}$ is: [2024]

9 : 7
4 : 3
5 : 3
8 : 1

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4

(A) $a_{c} = \frac{(m_{2} - m_{1}) g}{(m_{1} + m_{2})} \Rightarrow \frac{g}{8} = (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) g$

$\frac{1}{8} = (\frac{\frac{m_{2}}{m_{1}} - 1}{\frac{m_{2}}{m_{1}} + 1}) \Rightarrow \frac{m_{2}}{m_{1}} + 1 = 8 \frac{m_{2}}{m_{1}} - 8 \Rightarrow \frac{m_{2}}{m_{1}} = \frac{9}{7}$

Q 2 :
A wooden block of mass 5 kg rests on a soft horizontal floor. When an iron cylinder of mass 25 kg is placed on top of the block, the floor yields, and the block and the cylinder together go down with an acceleration of 0.1 ${ms}^{- 2}$ .

The action force of the system on the floor is equal to [2024].

294 N
196 N
297 N
291 N

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(4)

$30 g - N = 30 a$

Taking $g = 9.8 {m/s}^{2}$

$30 \times 9.8 - N = 30 \times 0.1$

$N = 291 N$

Q 3 :
A light string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ (where $m_{2} > m_{1}$ ). If the acceleration of the system is $\frac{g}{\sqrt{2}}$ , then the ratio of the masses $\frac{m_{1}}{m_{2}}$ is: [2024]

$\frac{\sqrt{3} + 1}{\sqrt{2} - 1}$
$\frac{1 + \sqrt{5}}{\sqrt{2} - 1}$
$\frac{1 + \sqrt{5}}{\sqrt{5} - 1}$
$\frac{\sqrt{2} - 1}{\sqrt{2} + 1}$

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4

(4)

$a = (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) g \Rightarrow \frac{g}{\sqrt{2}} = (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) g$

$(m_{1} + m_{2}) = \sqrt{2} m_{2} - \sqrt{2} m_{1}$

$\Rightarrow \frac{m_{1}}{m_{2}} = (\frac{\sqrt{2} - 1}{\sqrt{2} + 1})$

Q 4 :
A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg. The branch pulls the chain by a force equal to (if g = 10 $m / s^{2}$ ) [2024]

300 N
150 N
100 N
200 N

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(1)

Chain block system is in equilibrium, so T = 200 + 100 = 300 N.

Q 5 :
All surfaces shown in the figure are assumed to be frictionless and the pulleys and the string are light.

The acceleration of the block of mass 2 kg is [2024].

$g$
$\frac{g}{3}$
$\frac{g}{2}$
$\frac{g}{4}$

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(2)

By constrained motion

$- a_{1} + a_{2} + a_{2} = 0$

$a_{1} - 2 a_{2} = 0 or a_{2} = \frac{a_{1}}{2}$

$T - 2 g \sin 30 ° = 2 a_{1}$

$\Rightarrow T - g = 2 a_{1}$ ...(1)

$4 g - 2 T = 4 a_{2}$

$\Rightarrow 4 g - 2 T = 2 a_{1}$

$\Rightarrow 2 g - T = a_{1}$ ...(2)

Adding equation (1) and (2), $g = 3 a_{1} \Rightarrow a_{1} = \frac{g}{3}$

Q 6 :
Three blocks A, B, and C are pulled on a horizontal smooth surface by a force of 80 N as shown in the figure.

The tensions $T_{1}$ and $T_{2}$ in the string are respectively: [2024]

40 N, 64 N
60 N, 80 N
88 N, 96 N
80 N, 100 N

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(1)

$a = \frac{80}{10} = 8 {m/s}^{2}$

F.B.D of 5 kg

$T_{1} = 5 (a)$

$T_{1} = 5 (8) = 40 N$

$80 - T_{2} = 2 (8)$

$T_{2} = 80 - 16 = 64 N$

Q 7 :
In the given arrangement of a doubly inclined plane, two blocks of masses M and m are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of m, for which M = 10 kg will move down with an acceleration of 2 $m / s^{2}$ , is (take g = 10 $m / s^{2}$ and tan 37° = 3/4) [2024]

6.5 kg
4.5 kg
2.25 kg
9 kg

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(2)

For M block

$10 g \sin 53 ° - μ (10 g) \cos 53 ° - T = 10 \times 2$

$T = 80 - 15 - 20$

$T = 45 N$

For m block

$T - m g \sin 37 ° - μ m g \cos 37 ° = m \times 2$

$45 = 10 m$

$m = 4.5 kg$

Q 8 :
A light string passing over a smooth light fixed pulley connects two blocks of masses $m_{1}$ and $m_{2}$ .

If the acceleration of the system is g/8, then the ratio of masses is [2024].

$\frac{9}{7}$
$\frac{8}{1}$
$\frac{4}{3}$
$\frac{5}{3}$

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4

(1)

$a = \frac{(m_{1} - m_{2}) g}{(m_{1} + m_{2})} = \frac{g}{8}$

$8 m_{1} - 8 m_{2} = m_{1} + m_{2}$

$7 m_{1} = 9 m_{2}$

$\frac{m_{1}}{m_{2}} = \frac{9}{7}$

Q 9 :
Three blocks $M_{1}$ , $M_{2}$ , $M_{3}$ having masses 4 kg, 6 kg, and 10 kg respectively are hanging from a smooth pulley using rope 1, 2, and 3 as shown in the figure. The tension in the rope 1, $T_{1}$ , when they are moving upward with an acceleration of 2 ${ms}^{- 2}$ , is ________ N (if g = 10 $m / s^{2}$ ). [2024]

0%

(240)

FBD of $M_{1}$

$T_{1} - 200 = (4 + 6 + 10) \times 2$

$∴$ $T_{1} = 240 N$

Topic Question Set

Q 1 :
A light stretchable string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ . If the acceleration of the system is $\frac{g}{8}$ , then the ratio of the masses $\frac{m_{2}}{m_{1}}$ is: [2024]

Q 3 :
A light string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ (where $m_{2} > m_{1}$ ). If the acceleration of the system is $\frac{g}{\sqrt{2}}$ , then the ratio of the masses $\frac{m_{1}}{m_{2}}$ is: [2024]

Q 4 :
A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg. The branch pulls the chain by a force equal to (if g = 10 $m / s^{2}$ ) [2024]

Q 5 :
All surfaces shown in the figure are assumed to be frictionless and the pulleys and the string are light.

The acceleration of the block of mass 2 kg is [2024].

Q 6 :
Three blocks A, B, and C are pulled on a horizontal smooth surface by a force of 80 N as shown in the figure.

The tensions $T_{1}$ and $T_{2}$ in the string are respectively: [2024]

Q 8 :
A light string passing over a smooth light fixed pulley connects two blocks of masses $m_{1}$ and $m_{2}$ .

If the acceleration of the system is g/8, then the ratio of masses is [2024].

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Topic Question Set

Q 1 : A light stretchable string passing over a smooth light pulley connects two blocks of masses m1 and m2. If the acceleration of the system is g8, then the ratio of the masses m2m1 is: [2024]

Q 2 : A wooden block of mass 5 kg rests on a soft horizontal floor. When an iron cylinder of mass 25 kg is placed on top of the block, the floor yields, and the block and the cylinder together go down with an acceleration of 0.1 ms-2. The action force of the system on the floor is equal to [2024].

Q 3 : A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (where m2>m1). If the acceleration of the system is g2, then the ratio of the masses m1m2 is: [2024]

Q 4 : A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg. The branch pulls the chain by a force equal to (if g = 10 m/s2) [2024]

Q 5 : All surfaces shown in the figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is [2024].

Q 6 : Three blocks A, B, and C are pulled on a horizontal smooth surface by a force of 80 N as shown in the figure. The tensions T1 and T2 in the string are respectively: [2024]

Q 8 : A light string passing over a smooth light fixed pulley connects two blocks of masses m1 and m2. If the acceleration of the system is g/8, then the ratio of masses is [2024].

Q 9 : Three blocks M1, M2, M3 having masses 4 kg, 6 kg, and 10 kg respectively are hanging from a smooth pulley using rope 1, 2, and 3 as shown in the figure. The tension in the rope 1, T1, when they are moving upward with an acceleration of 2 ms-2, is ________ N (if g = 10 m/s2). [2024]

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Q 1 :
A light stretchable string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ . If the acceleration of the system is $\frac{g}{8}$ , then the ratio of the masses $\frac{m_{2}}{m_{1}}$ is: [2024]

Q 3 :
A light string passing over a smooth light pulley connects two blocks of masses $m_{1}$ and $m_{2}$ (where $m_{2} > m_{1}$ ). If the acceleration of the system is $\frac{g}{\sqrt{2}}$ , then the ratio of the masses $\frac{m_{1}}{m_{2}}$ is: [2024]

Q 4 :
A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg. The branch pulls the chain by a force equal to (if g = 10 $m / s^{2}$ ) [2024]

Q 5 :
All surfaces shown in the figure are assumed to be frictionless and the pulleys and the string are light.

The acceleration of the block of mass 2 kg is [2024].

Q 6 :
Three blocks A, B, and C are pulled on a horizontal smooth surface by a force of 80 N as shown in the figure.

The tensions $T_{1}$ and $T_{2}$ in the string are respectively: [2024]

Q 8 :
A light string passing over a smooth light fixed pulley connects two blocks of masses $m_{1}$ and $m_{2}$ .

If the acceleration of the system is g/8, then the ratio of masses is [2024].