Q: Momentum of a particle, travelling on a straight line, changes with time, as shown in the figure. Find the maximum force acting on the particle at any instant.

F=dtdP= slope of P−t graph.=20 N

Question 1

A uniform wire is bent into a shape shown in figure. Segments AB and ED are straight, having length 2R each, lying in a horizontal plane and the segment BCD is a semicircle of radius R. Find the distance of the COM of the wire from centre O of the circle.

Accepted Answer

Here is the solution,

Question 2

A smooth rod of length L=2R is leaning against a semi cylinder of radius R, which is placed on a smooth horizontal surface. In the position shown, θ=45∘. The system is released from this position. Find the displacement of the semi cylinder by the time end B of the rod touches it. Both cylinder and rod have the same mass.

Accepted Answer

210​(32​−5​)R​

Question 3

A disc of radius r is uniform. A square-hole of side length l=2​r​ is punched in the disc, as shown. One corner of the hole is at centre O of the disc and the other corner is at A on the circumference. The diagonal OA of the square is y-axis and O is the origin. Find the co-ordinates of the COM of the disc with hole.

Accepted Answer

Here is the solution,

Question 4

A rope has length 3L and is made of three uniform segments of length L each. Mass of the two endsegments are m and 2m. The mid segment has mass 1.5 m. The rope is placed over a smooth equilateral wedge fixed on a horizontal table. The rope stays in equilibrium. Find y co-ordinate of the COM of the rope, measured from the apex point O.

Accepted Answer

Here is the solution,

Question 5

A conical container has a circular base of radius R and height 4R. It is filled with a liquid of density d. Below the cone, there is a cylindrical container of radius R. Base of the cylinder is at a depth 2R below the apex of the cone. Cap at the apex of the cone is opened and the liquid slowly drains into the cylindrical containers. Calculate work done by gravity in the process.

Accepted Answer

Here is the solution,

Question 6

A projectile of mass m is projected at an angle θ to the horizontal at speed u. Find change in its momentum by the time(i) it reaches the top point of its trajectory.(ii) it is about to hit the ground.

Accepted Answer

Here is the solution,

Question 7

Momentum of a particle, travelling on a straight line, changes with time, as shown in the figure. Find the maximum force acting on the particle at any instant.

Accepted Answer

F=dtdP​= slope of P−t graph.=20 N

Question 8

A car of mass M enters a semi-circular track at speed v and exits out of it at speed v. The track has radius R. Find the average force experienced by the car on the track.

Accepted Answer

Here is the solution,

Question 9

Wind is blowing horizontally at a speed v. Density of air is ρ. Calculate force experienced by a vertical wall of area A. Assume that the air spreads parallel to the surface of the wall after striking it. How will the force change if speed increases to 2v ?

Accepted Answer

Here is the solution,

Question 10

A wide container of negligible mass is placed on a weighing scale. A tank at height H pours water on it. Assume that water comes out of the tank at negligible speed and at a rate of μkgs−1. The falling water does not splash and spreads uniformly on the container. Find the reading of the weighing scale at a time t afler the water starts pouring into the container.

Accepted Answer

Mass of water accumulated in the container at time t  is μt .∴ Weight of water in container, W=μt⋅gApart from this weight, the falling water also exerts a thrust force on the container.Speed of water hitting the container, v=2gH​Mass of water hitting the container in unit time =μ.Water particle does not bounce back.∴F= rate of change of momentum  =μ2gH​ ∴ Reading of scale =μ2gH​+μgt

Question 11

An army person fires 50 g bullets horizontally from a machine gun. Bullets leave the gun at a speed of 1kms−1 and he fires 20 bullets in 4 s. Find the average horizontal force that he exters on the gun to hold it.

Accepted Answer

Here is the solution,

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Solutions for Physics for JEE Main and Advanced Mechanics 2 by Shashi Bhushan Tiwari

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