(B) Let $m_2 = 300 \ g$ and $m_1 = 200 \ g$. The angle of inclination is $\theta = 30^{\circ}$.For the block of mass $m_2$,the equation of motion is:

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(B) Let $m_2 = 300 \ g$ and $m_1 = 200 \ g$. The angle of inclination is $\theta = 30^{\circ}$.For the block of mass $m_2$,the equation of motion is: $m_2 g \sin \theta - T = m_2 a$ $(i)$For the block of mass $m_1$,the equation of motion is: $T - m_1 g \sin \theta = m_1 a$ (ii)Adding equations $(i)$ and (ii),we get:$(m_2 - m_1) g \sin \theta = (m_1 + m_2) a$$a = \frac{(m_2 - m_1) g \sin \theta}{m_1 + m_2}$Substituting the values: $a = \frac{(300 - 200) g \sin 30^{\circ}}{300 + 200}$$a = \frac{100 \times g \times 0.5}{500} = \frac{50}{500} g = \frac{1}{10} g$$a = 0.1 g = 10 \% \text{ of } g$.

Class 11 Physics Newton's Laws of Motion and Friction Motion of Body (or Connected Bodies) on an inclined plane

Medium

$A$ double inclined plane as shown in the figure has a fixed horizontal base and smooth faces with the same angle of inclination of $30^{\circ}$. $A$ block of mass $m_2 = 300 \ g$ is on one face and is connected by a cord passing over a frictionless pulley to a second block of mass $m_1 = 200 \ g$ kept on the other face. The acceleration with which the system of the blocks moves is ........ $\%$ of acceleration due to gravity $(g)$.

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A
$5$
B
$10$
C
$15$
D
$20$

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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) on an inclined plane

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Three blocks are connected by massless strings on a frictionless inclined plane of $30^{\circ}$ as shown in the figure. $A$ force of $104 \,N$ is applied upward along the incline to mass $m_3$ causing an upward motion of the blocks. What is the acceleration of the blocks (in $\,m / s^2$)? (Assume, acceleration due to gravity, $g=10 \,m / s^2$ )

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In the figure shown,$A$ and $B$ are free to move. All the surfaces are smooth. Then for $(0 < \theta < 90^o)$:

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$A$ frictionless wire $AB$ is fixed on a sphere of radius $R$. $A$ very small spherical ball slips on this wire. The time taken by this ball to slip from $A$ to $B$ is

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$A$ body sliding on a smooth inclined plane requires $4$ seconds to reach the bottom starting from rest at the top. How much time does it take to cover one-fourth distance starting from rest at the top?

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Find the acceleration of the system shown in the figure.

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In the figure shown,$A$ and $B$ are free to move. All the surfaces are smooth. Then for $(0 < \theta < 90^o)$:

$A$ frictionless wire $AB$ is fixed on a sphere of radius $R$. $A$ very small spherical ball slips on this wire. The time taken by this ball to slip from $A$ to $B$ is

$A$ body sliding on a smooth inclined plane requires $4$ seconds to reach the bottom starting from rest at the top. How much time does it take to cover one-fourth distance starting from rest at the top?

Find the acceleration of the system shown in the figure.

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