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A painter is applying force himself to raise him and the box with an acceleration of 5 m/s^{2} by a massless rope and pulley arrangement as shown in figure. Mass of painter is 100kg and that of box is 50kg. If g = 10 m/s^{2}, then :
Select one or more:
For painter :
.....(1)
For the system;
..(2)
where; m = 100 kg
and
The correct answers are: tension in the rope is 1125 N, force of contact between the painter and the floor is 375 N
Two blocks A and B of equal masses m kg each are connected by a light thread, which passes over a massless pulley as shown in the figure. Both the blocks lies on wedge of mass m kg. Assume friction to be absent everywhere and both the blocks to be always in contact with the wedge. The wedge lying over smooth horizontal surface is pulled towards right with constant acceleration a (m/s^{2}).
(g is acceleration due to gravity)
Select one or more:
The FBD of A and B are
Applying Newton's second law to block A and B along normal to inclined surface
Solving
For N_{A} to be non zero
or
The correct answers are:
Normal reaction on A is
Normal reaction on B is
A light inextensible string connects a block of mass m and top of wedge of mass M. The string is parallel to inclined surface and the inclined surface makes and angle θ with horizontal as show in the figure. All surfaces are smooth. Now a constant horizontal force of minimum magnitude F is applied to wedge towards right such that the normal reaction on block exerted by wedge just becomes zero.
Select one or more:
If a is acceleration of wedge, from
Two smooth blocks are placed at a smooth corner as shown in the figure. Both the blocks are having mass m. We apply a force F on the small block m. Block A presses the block B in the normal direction, due to which pressing force on vertical wall will increase, and pressing force on the horizontal wall decrease, as we increase F (θ = 37º with horizontal). As soon as the pressing force on the horizontal wall by block B becomes zero, it will loose the contact with the ground. If the value of F is further increased, the block B will accelerate in upward direction and simultaneously the block A will move toward right.
Select one or more:
For equilibrium of block (A)
To lift block B from ground
To keep regular contact
The correct answer is: a_{B} = 3a/4
Two blocks of mass M and m, are used to compress two different massless springs as shown in the figure. The left spring is compressed by 3cm, while the right spring is compressed by an unknown amount. The system is at rest and all contact surfaces are smooth. Which of the following statements are true?
Select one or more:
Let F be the force exerted by mass m on mass M.
FBD of mass M
F = k_{1}x_{1} = 2 × 3 = 6N
FBD of mass m
k_{2}x_{2} = F = 6N to the left
Hence the force exerted on block of mass m be the right spring (k_{2}x_{2}) is 6 N to the left. From FBD, the normal reaction (F) between blocks is 6 N.
As system is at rest, net force on block of mass m is zero.
The correct answers are: The force exerted on block of mass m by the right spring is 6N to left, The net force on block of mass m is zero, The normal force exerted by block of mass m on block of mass M is 6 N
Two blocks A and B of equal mass m are connected through a massless string and arrangement as shown in the figure. The wedge is fixed on horizontal surface. Friction is absent everywhere. When the system is released from rest.
Select one or more:
Let a be acceleration of system and T be tension in, the string.
F.B.D. of block A
F.B.D. of block B
Adding equation (1) and (2) we get
from equation (1) ;
T = mg/4
The correct answers are: tension in string is mg/4, acceleration of A is 3g/4
Figure shows two block A and B connected to an ideal pulley string system. In this system when bodies are released then : (neglect friction and take g = 10m/s^{2})
Select one or more:
Applying NLM on 40kg block
For 10kg block T = 10 × 4a
Solving a = 2m/s^{2}
T = 80 N
The correct answers are: Acceleration of block A is 2 m/s^{2}, Tension in string connected to block B is 80 N
In the figure shown all the surfaces are smooth. All the blocks A, B and C are movable, xaxis is horizontal and yaxis is vertical as shown. Just after the system is released from the position as shown.
Select one or more:
There is no horizontal force on block A, therefore it does not move in xdirection, whereas there is net downwards force (mg – N) is acting on it, making its acceleration along negative ydirection.
Block B moves downwards as well as in negative xdirection. Downward acceleration of A and B will be equal due to constrain, thus w.r.t. B, A moves in positive xdirection.
Due to the component of normal exerted by C on B, it moves in negative xdirection.
The force acting vertically downwards on block B are mg and N_{A} (normal reaction due to block A). Hence the component of net force on block B along the inclined surface of B is greater than mg sin θ. Therefore the acceleration of ‘B’ relative to ground directed along the inclined surface of ‘C’ is greater than g sin θ.
The correct answers are: Acceleration of ‘A’ relative to ground is in negative ydirection, Acceleration of ‘A’ relative to B is in positive xdirection, The horizontal acceleration of ‘B’ relative to ground is in negative xdirection., The acceleration of ‘B’ relative to ground directed along the inclined surface of ‘C’ is greater than gsinθ
A block of mass m is placed on a wedge. The wedge can be accelerated in four manners marked as (1), (2), (3) and (4) as shown. If the normal reactions in situation (1), (2), (3) and (4) are N_{1}, N_{2}, N_{3} and N_{4} respectively and acceleration with which the block slides on the wedge in situations are b_{1}, b_{2}, b_{3} and b_{4} respectively then :
Select one or more:
1.
Balancing forces perpendicular to incline
2.
Similarly for this case get
3.
Similarly for this case get
4.
Similarly for this case get,
The correct answers are: N_{3} > N_{1} > N_{2} > N_{4} , b_{2} > b_{3} > b_{4} > b_{1}
A cylinder of mass M and radius R is resting on two corner edges A and B as shown in the figure. The normal reaction at the edges A and B are : (Neglect friction)
Select one or more:
The correct answers are:
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