(C) Let $R$ be the upward buoyant force acting on the balloon.Case $1$: The balloon is moving down with acceleration $a_0$.The equation of motion is:

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(C) Let $R$ be the upward buoyant force acting on the balloon.Case $1$: The balloon is moving down with acceleration $a_0$.The equation of motion is: $Mg - R = Ma_0$ ....$(i)$Case $2$: After removing mass $m$,the balloon moves up with acceleration $2a_0$.The equation of motion is: $R - (M - m)g = (M - m)(2a_0)$ ....(ii)Adding equations $(i)$ and (ii):$(Mg - R) + (R - (M - m)g) = Ma_0 + (M - m)(2a_0)$$Mg - Mg + mg = Ma_0 + 2Ma_0 - 2ma_0$$mg = 3Ma_0 - 2ma_0$$mg + 2ma_0 = 3Ma_0$$m(g + 2a_0) = 3Ma_0$$m = \frac{3Ma_0}{g + 2a_0}$

Class 11 Physics Newton's Laws of Motion and Friction Motion of Body (or Connected Bodies in horizontal or vertical) (by String or Contact)

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$A$ balloon carrying some sand of mass $M$ is moving down with a constant acceleration $a_0$. The mass $m$ of sand to be removed so that the balloon moves up with double the acceleration $2a_0$ is:

AP EAMCET 2024 All AP EAMCET

A
$m=\frac{2 M a_0}{a_0+g}$
B
$m=\frac{2 M a_0}{a_0-g}$
C
$m=\frac{3 M a_0}{g+2 a_0}$
D
$m=\frac{3 M a_0}{g-2 a_0}$

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Class 11

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Newton's Laws of Motion and Friction

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Motion of Body (or Connected Bodies in horizontal or vertical) (by String or Contact)

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Two masses $M$ and $m$ are connected by a weightless string. They are pulled by a force $F$ on a frictionless horizontal surface as shown in the figure. The tension in the string will be

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$A$ uniform rope of mass $1.0 \ kg$ is connected to a box of mass $2.0 \ kg$,which is placed on a smooth horizontal surface. The free end of the rope is pulled horizontally by a force of $6 \ N$. Find the tension at the midpoint of the rope. ............ $N$

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$A$ mass of $1 \ kg$ is suspended by means of a thread. The system is
$(i)$ lifted up with an acceleration of $4.9 \ ms^{-2}$
(ii) lowered with an acceleration of $4.9 \ ms^{-2}$.
The ratio of tension in the first and second case is

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Three blocks are connected as shown in the figure on a horizontal frictionless table. If $m_1 = 1 \, kg, m_2 = 8 \, kg, m_3 = 27 \, kg$ and $T_3 = 36 \, N$,then $T_2$ will be ............ $N$.

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What is the minimum acceleration with which a person can slide down a rope,if the breaking strength of the rope is $\frac{2}{3}$ of the person's weight?

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$A$ balloon carrying some sand of mass $M$ is moving down with a constant acceleration $a_0$. The mass $m$ of sand to be removed so that the balloon moves up with double the acceleration $2a_0$ is:

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Two masses $M$ and $m$ are connected by a weightless string. They are pulled by a force $F$ on a frictionless horizontal surface as shown in the figure. The tension in the string will be

$A$ uniform rope of mass $1.0 \ kg$ is connected to a box of mass $2.0 \ kg$,which is placed on a smooth horizontal surface. The free end of the rope is pulled horizontally by a force of $6 \ N$. Find the tension at the midpoint of the rope. ............ $N$

$A$ mass of $1 \ kg$ is suspended by means of a thread. The system is$(i)$ lifted up with an acceleration of $4.9 \ ms^{-2}$(ii) lowered with an acceleration of $4.9 \ ms^{-2}$.The ratio of tension in the first and second case is

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What is the minimum acceleration with which a person can slide down a rope,if the breaking strength of the rope is $\frac{2}{3}$ of the person's weight?

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$A$ mass of $1 \ kg$ is suspended by means of a thread. The system is
$(i)$ lifted up with an acceleration of $4.9 \ ms^{-2}$
(ii) lowered with an acceleration of $4.9 \ ms^{-2}$.
The ratio of tension in the first and second case is