(C) For figure $(a)$: The block $m_1$ is on a smooth horizontal surface and $m_2$ is hanging. The equations of motion are:$T = m_1 a_1$ ... $(i)$$m_2

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$\frac{40}{7} \ ms^{-2}, \frac{10}{7} \ ms^{-2}$

(C) For figure $(a)$: The block $m_1$ is on a smooth horizontal surface and $m_2$ is hanging. The equations of motion are:$T = m_1 a_1$ ... $(i)$$m_2 g - T = m_2 a_1$ ... (ii)Adding $(i)$ and (ii),we get $m_2 g = (m_1 + m_2) a_1$,so $a_1 = \frac{m_2 g}{m_1 + m_2}$.Substituting the values: $a_1 = \frac{4 \times 10}{3 + 4} = \frac{40}{7} \ ms^{-2}$.For figure $(b)$: This is an Atwood machine. The acceleration $a_2$ is given by:$a_2 = \left( \frac{m_2 - m_1}{m_1 + m_2} \right) g$Substituting the values: $a_2 = \left( \frac{4 - 3}{3 + 4} \right) \times 10 = \frac{1}{7} \times 10 = \frac{10}{7} \ ms^{-2}$.Thus,$a_1 = \frac{40}{7} \ ms^{-2}$ and $a_2 = \frac{10}{7} \ ms^{-2}$.

Class 11 Physics Newton's Laws of Motion and Friction Mix Examples-Newton's Laws of Motion and Friction

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Two situations are shown in figures $(a)$ and $(b)$. In each case,$m_1 = 3 \ kg$ and $m_2 = 4 \ kg$. If $a_1$ and $a_2$ are the respective accelerations of the blocks in these situations,then the values of $a_1$ and $a_2$ are respectively [ $g = 10 \ ms^{-2}$ ]

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A
$\frac{20}{7} \ ms^{-2}, \frac{10}{7} \ ms^{-2}$
B
$\frac{10}{7} \ ms^{-2}, \frac{25}{7} \ ms^{-2}$
C
$\frac{40}{7} \ ms^{-2}, \frac{10}{7} \ ms^{-2}$
D
$\frac{30}{7} \ ms^{-2}, \frac{5}{7} \ ms^{-2}$

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Newton's Laws of Motion and Friction

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Mix Examples-Newton's Laws of Motion and Friction

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Two balls of masses $m_1$ and $m_2$ are separated from each other by a powder charge placed between them. The whole system is at rest on the ground. Suddenly,the powder charge explodes and the masses are pushed apart. The mass $m_1$ travels a distance $s_1$ and stops. If the coefficients of friction between the balls and the ground are the same,the mass $m_2$ stops after travelling the distance:

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Three weights $A, B$ and $C$ are connected by strings as shown in the figure. The system moves over a frictionless pulley. The tension in the string connecting $A$ and $B$ is (where $g$ is acceleration due to gravity):

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$A$ bouncing ball of mass $200 \,g$ falls from a height of $5 \,m$ onto a horizontal ground. After every impact with the ground, the velocity of the ball decreases by $\frac{1}{2}$ times. The total momentum the ball imparts to the ground after $3$ impacts is (Let $g=10 \,m/s^2$):

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Explain why
$(a)$ a horse cannot pull a cart and run in empty space,
$(b)$ passengers are thrown forward from their seats when a speeding bus stops suddenly,
$(c)$ it is easier to pull a lawn mower than to push it,
$(d)$ a cricketer moves his hands backwards while holding a catch.

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$A$ system consists of three masses $m_1, m_2$ and $m_3$ connected by a string passing over a pulley $P$. The mass $m_1$ hangs freely and $m_2$ and $m_3$ are on a rough horizontal table (the coefficient of friction $= \mu$). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_1$ is (Assume $m_1 = m_2 = m_3 = m$)

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Two situations are shown in figures $(a)$ and $(b)$. In each case,$m_1 = 3 \ kg$ and $m_2 = 4 \ kg$. If $a_1$ and $a_2$ are the respective accelerations of the blocks in these situations,then the values of $a_1$ and $a_2$ are respectively [ $g = 10 \ ms^{-2}$ ]

Similar Questions

Three weights $A, B$ and $C$ are connected by strings as shown in the figure. The system moves over a frictionless pulley. The tension in the string connecting $A$ and $B$ is (where $g$ is acceleration due to gravity):

$A$ bouncing ball of mass $200 \,g$ falls from a height of $5 \,m$ onto a horizontal ground. After every impact with the ground, the velocity of the ball decreases by $\frac{1}{2}$ times. The total momentum the ball imparts to the ground after $3$ impacts is (Let $g=10 \,m/s^2$):

Explain why$(a)$ a horse cannot pull a cart and run in empty space,$(b)$ passengers are thrown forward from their seats when a speeding bus stops suddenly,$(c)$ it is easier to pull a lawn mower than to push it,$(d)$ a cricketer moves his hands backwards while holding a catch.

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Explain why
$(a)$ a horse cannot pull a cart and run in empty space,
$(b)$ passengers are thrown forward from their seats when a speeding bus stops suddenly,
$(c)$ it is easier to pull a lawn mower than to push it,
$(d)$ a cricketer moves his hands backwards while holding a catch.