Physics-
General
Easy
Question
Two men ‘A’ and ‘B’ are standing on a plank. ‘B’ is at the middle of the plank and ‘A’ is the left end of the plank. The surface between plank and ground is smooth. System is initially at rest and masses are as shown in figure. ‘A’ and ‘B’ starts moving such that the position of ‘B’ remains fixed with respect to ground. Then the point where A meets B is located at
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)
- the middle of the plank
- 30 cm from the left end of the plank
- the right end of the plank
- None of these
The correct answer is: the middle of the plank
Related Questions to study
physics-
In a vertical plane inside a smooth hollow thin tube a block of same mass as that of tube is released as shown in figure. When it is slightly disturbed, it moves towards right. By the time the block reaches the right end of the tube then the displacement of the tube will be (where ‘R’ is mean radius of tube). Assume that the tube remains in vertical plane.
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)
In a vertical plane inside a smooth hollow thin tube a block of same mass as that of tube is released as shown in figure. When it is slightly disturbed, it moves towards right. By the time the block reaches the right end of the tube then the displacement of the tube will be (where ‘R’ is mean radius of tube). Assume that the tube remains in vertical plane.
![](data:image/png;base64,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)
physics-General
physics-
The figure shows a hollow cube of side 'a' of volume V. There is a small chamber of volume
in the cube as shown. This chamber is completely filled by m kg of water. Water leaks through a hole H. Then the work done by gravity in this process assuming that the complete water finally lies at the bottom of the cube is :
![](data:image/png;base64,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)
The figure shows a hollow cube of side 'a' of volume V. There is a small chamber of volume
in the cube as shown. This chamber is completely filled by m kg of water. Water leaks through a hole H. Then the work done by gravity in this process assuming that the complete water finally lies at the bottom of the cube is :
![](data:image/png;base64,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)
physics-General
physics-
On a smooth carom board, a coin moving in negative y-direction with a speed of 3 m/s is being hit at the point (4, 6) by a striker moving along negative x-axis. The line joining centres of the coin and the striker just before the collision is parallel to x-axis. After collision the coin goes into the hole located at the origin. Masses of the striker and the coin are equal. Considering the collision to be elastic, the initial and final speeds of the striker in m/s will be :
![](data:image/png;base64,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)
On a smooth carom board, a coin moving in negative y-direction with a speed of 3 m/s is being hit at the point (4, 6) by a striker moving along negative x-axis. The line joining centres of the coin and the striker just before the collision is parallel to x-axis. After collision the coin goes into the hole located at the origin. Masses of the striker and the coin are equal. Considering the collision to be elastic, the initial and final speeds of the striker in m/s will be :
![](data:image/png;base64,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)
physics-General
physics-
A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from
to
at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic (g = 10
) If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is :–
![](data:image/png;base64,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)
A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from
to
at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic (g = 10
) If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is :–
![](data:image/png;base64,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)
physics-General
physics-
A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from
to
at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic (g = 10
) The speed of the block at point C, immediately before it leaves the second incline is :–
![](data:image/png;base64,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)
A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from
to
at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic (g = 10
) The speed of the block at point C, immediately before it leaves the second incline is :–
![](data:image/png;base64,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)
physics-General
physics-
A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from
to
at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic (g = 10
) The speed of the block at point B immediately after it strikes the second incline is :–
![](data:image/png;base64,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)
A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from
to
at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic (g = 10
) The speed of the block at point B immediately after it strikes the second incline is :–
![](data:image/png;base64,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)
physics-General
physics-
Look at the drawing given in the figure which has been drawn with ink of uniform line– thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments in m. The mass of the ink used to draw the outer circle is 6m. The coordinates of the centres of the different parts are : outer circle (0, 0), left inner circle (– a, a), right inner circle (a, a), vertical line (0, 0) and horizontal line (0, – a). The y–coordinates of the centre of mass of the ink in this drawing is :–
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)
Look at the drawing given in the figure which has been drawn with ink of uniform line– thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments in m. The mass of the ink used to draw the outer circle is 6m. The coordinates of the centres of the different parts are : outer circle (0, 0), left inner circle (– a, a), right inner circle (a, a), vertical line (0, 0) and horizontal line (0, – a). The y–coordinates of the centre of mass of the ink in this drawing is :–
![](data:image/png;base64,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)
physics-General
physics-
Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are v and 2v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other that at A, these two particles will again reach the point A ?
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)
Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. Their tangential velocities are v and 2v, respectively, as shown in the figure. Between collisions, the particles move with constant speeds. After making how many elastic collisions, other that at A, these two particles will again reach the point A ?
![](data:image/png;base64,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)
physics-General
maths-
If the line x + y = 1 touches the parabola y2 – y + x = 0 and h = value of x where | x | is not differentiable, k =
cos2nx, where
. then the point of contact is
If the line x + y = 1 touches the parabola y2 – y + x = 0 and h = value of x where | x | is not differentiable, k =
cos2nx, where
. then the point of contact is
maths-General
maths-
Two parabolas y2 = 4a (x –λ1) and x2 = 4a (y –
2) always touch each other,
1 and λ 2 being variable parameters. Then, their points of contact lie on a
Two parabolas y2 = 4a (x –λ1) and x2 = 4a (y –
2) always touch each other,
1 and λ 2 being variable parameters. Then, their points of contact lie on a
maths-General
maths-
If t1 and t2 be the ends of a focal chord of the parabola y2 = 4ax, then the equation t1x2 + ax + t2 = 0 has
If t1 and t2 be the ends of a focal chord of the parabola y2 = 4ax, then the equation t1x2 + ax + t2 = 0 has
maths-General
maths-
If two distinct chords drawn from the point (4, 4) on the parabola y2 = 4ax are bisected on the line y = mx, then the set of value of m is given by -
If two distinct chords drawn from the point (4, 4) on the parabola y2 = 4ax are bisected on the line y = mx, then the set of value of m is given by -
maths-General
maths-
If normal at point P on parabola y2 = 4ax, (a > 0) meet it again at Q is such a way that OQ is of minimum length where O is vertex of parabola, then ΔOPQ is
If normal at point P on parabola y2 = 4ax, (a > 0) meet it again at Q is such a way that OQ is of minimum length where O is vertex of parabola, then ΔOPQ is
maths-General
maths-
AB is a chord of the parabola y2 = 4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the x-axis is-
AB is a chord of the parabola y2 = 4ax with vertex at A. BC is drawn perpendicular to AB meeting the axis at C. The projection of BC on the x-axis is-
maths-General
maths-
The locus of point ‘P’ where the three normals drawn from it on the parabola y2 = 4ax are such that two of them make complementary angles with x-axis is
The locus of point ‘P’ where the three normals drawn from it on the parabola y2 = 4ax are such that two of them make complementary angles with x-axis is
maths-General