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*Answer can only contain numeric values

QUESTION: 1

A 1.5*kg* box is initially at rest on a horizontal surface when at * t* = 0 a horizontal force (with

The coefficient of kinetic friction between the box and the surface is :

Solution:

The correct answer is: 0.24

*Answer can only contain numeric values

QUESTION: 2

In figure shown, the coefficient of static friction between *C* and ground is 0.5, coefficient of static friction between *A* and *B* is 0.25, coefficient of static friction between *B* and *C* is zero. Find the minimum value of force * F* (is

Solution:

The F.B.D. of *A* and *B* are

force of friction

For sliding to start between *A* and *B*, the frictional

Apply Newton's second law of system *A* + *B
*

Apply Newton's second law of

from (1) and (2)

The correct answer is: 15

*Answer can only contain numeric values

QUESTION: 3

A mass *m* is supported as shown in the figure by ideal strings connected to a rigid wall and to a mass 3*m* at rest on a fixed horizontal surface. The string connected to larger mass is horizontal, that connected to smaller mass is vertical and the one connected to wall makes an angle 60° with horizontal. Then the minimum coefficient of static friction between the larger mass and the horizontal surface that permits the system to remain in equilibrium in the situation shown is given by

Find the value of * n*.

Solution:

At the instant 3*m* is about to slip, tension in all the strings are as shown

The correct answer is: 3

*Answer can only contain numeric values

QUESTION: 4

In the system shown in figure the friction coefficient between ground and bigger block is μ. There is no friction between both the blocks. The string connecting both the block is light; all three pulleys are light and frictionless. Then the minimum limiting value of μ so that the system remains in equilibrium is :

Solution:

In equilibrium

The correct answer is: 0.667

*Answer can only contain numeric values

QUESTION: 5

A block of mass 1 kg is placed on a rough horizontal surface. A spring is attached to the block whose other end is joined to a rigid wall, as shown in the figure. A horizontal force is applied on the block so that it remains at rest while the spring is elongated by * x. *Let

For a particular

The coefficient of friction between the block and the horizontal surface is :

Solution:

The correct answer is: 0.1

*Answer can only contain numeric values

QUESTION: 6

The rear side of a truck is open and a box of 40*kg* mass is placed 5*m* away from the open and as shown. The coefficient of friction between the box and the surface below it is 0.15. On a straight road, the truck starts from rest and accelerates with 2*ms*^{–2}. At what distance (in *m*.) from the starting point does the box fall off the truck (i.e. distance traveled by the truck)? [Ignore the size of the box]

Solution:

In the reference frame of the truck *FBD* of 40 kg block

Net force = *ma* – µ*N
*

This acceleration of the block in reference frame of truck so time taken by box to fall down from truck

So distance moved by the truck

The correct answer is: 20

*Answer can only contain numeric values

QUESTION: 7

A block of mass *m* is placed on top of a block of mass 2*m* which in turn is placed on fixed horizontal surface. The coefficient of friction between all surfaces is µ = 1. A massless string is connected to each mass and wraps halfway around a massless and frictionless pulley, as shown in the figure. The pulley is pulled by horizontal force of magnitude *F* = 6*mg* towards right as shown. If the magnitude of acceleration of pulley is x/2 m/s^{2}. Fill the value of * x*. (Take

Solution:

The F.B.D. of both blocks is as shown.

Hence, * x* = 25

The correct answer is: 25

*Answer can only contain numeric values

QUESTION: 8

A block of mass 5*kg* is placed on a rough horizontal surface of a moving compartment. It is seen by an observer sitting inside the compartment, that a force of 10*N* is required in horizontal direction to move the box in a direction parallel to the motion of compartment. While a force of 20*N* is required in horizontal direction to move the box in opposite direction. If coefficient of friction between the block and the surface is x/10 then find out value of * x*.

Solution:

As seen from an inside observer, the forces acting on the block are pseudo force, frictional force and the applied force.

When the applied force is in the direction of pseudo force (in this case force will be required to move the block)

10 + pseudo force = µ*mg* ...(1)

When the applied force is opposite to the pseudo force,

20 – pseudo force = µ**·***m ·g* ...(2)

Adding (1) and (2)

30 = 2µ

∴ µ = 0.3

⇒

The correct answer is: 3

*Answer can only contain numeric values

QUESTION: 9

In the figure shown, the coefficient of static friction between *B* and the wall is 2/3 and the coefficient of kinetic friction between *B* and the wall is 1/3. Other contacts are smooth. Find the minimum force *F* required to lift *B*, up. It is then * x* is. Mass of

Solution:

The F.B.D. of *A* and *B* are

For *A* to be in equilibrium

for *B* to just lift off

For horizontal equilibrium of *B
*

From (2) and (3)

From equation (1)

The correct answer is: 3

*Answer can only contain numeric values

QUESTION: 10

A block of 7 *kg* is placed on a rough horizontal surface and is pulled through a variable force *F *(in *N*) = 5*t*, where * t* is time is second, and an angle of 37° with the horizontal as shown in figure. The coefficient of static friction of the block with the surface is one. If the force starts acting at

Solution:

The block begins to slide if

The correct answer is: 10

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