Question
Two blocks A and B of equal mass m are connected through a massless string and arranged as shown in figure. Friction is absent everywhere. When the system is released from rest
- tension in string is
![mg over 2](data:image/png;base64,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)
- tension in string is
![mg over 4](data:image/png;base64,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)
- acceleration of A is
![fraction numerator text g end text over denominator 2 end fraction](data:image/png;base64,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)
- acceleration of A is
![3 over 4 g](data:image/png;base64,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)
The correct answer is: acceleration of A is ![3 over 4 g](data:image/png;base64,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)
Related Questions to study
The velocity-time graph of a particle in linear motion is shown. Both
and
are in SI units. What is the displacement of the particle from the origin after 8 s?
![](data:image/png;base64,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)
The velocity-time graph of a particle in linear motion is shown. Both
and
are in SI units. What is the displacement of the particle from the origin after 8 s?
![](data:image/png;base64,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)
If
has a real solution then
If
has a real solution then
In the following arrangement the system is initially at rest. The 5 kg block is now released. Assuming the pulleys and string to be massless and smooth, the acceleration of blocks is
In the following arrangement the system is initially at rest. The 5 kg block is now released. Assuming the pulleys and string to be massless and smooth, the acceleration of blocks is
The equation
has
The equation
has
A particle is moving along the circle
in anticlockwise direction. The x–y plane is a rough horizontal stationary surface. At the point
, the unit vector in the direction of friction on the particle is
A particle is moving along the circle
in anticlockwise direction. The x–y plane is a rough horizontal stationary surface. At the point
, the unit vector in the direction of friction on the particle is
If
then the solution set in
is
If
then the solution set in
is
A man of mass 50 kg is pulling on a plank of mass 100 kg kept on a smooth floor as shown with force of 100 N. If both man & plank move together, find force of friction acting on man
A man of mass 50 kg is pulling on a plank of mass 100 kg kept on a smooth floor as shown with force of 100 N. If both man & plank move together, find force of friction acting on man
Solutions in the given Interval: The value of
satisfying
are
Solutions in the given Interval: The value of
satisfying
are
The area of the equilateral triangle which containing three coins of unity radius is
![](data:image/png;base64,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)
The area of the equilateral triangle which containing three coins of unity radius is
![](data:image/png;base64,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)
If
then x =
If
then x =
The curves
and
cut each other at the common point at an angle
The curves
and
cut each other at the common point at an angle
Block A of mass m is placed over a wedge B of same mass m. Assuming all surfaces to be smooth. The displacement of block A in 1 s if the system is released from rest is
Block A of mass m is placed over a wedge B of same mass m. Assuming all surfaces to be smooth. The displacement of block A in 1 s if the system is released from rest is
If
and
then the
are
If
and
then the
are
In the figure shown block B moves down with a velocity 10 m/s. The velocity of A in the position shown is
In the figure shown block B moves down with a velocity 10 m/s. The velocity of A in the position shown is