Author name: PCM TUTORIALS

Moment of Inertia of Rod having non-uniform, linearly increasing mass density

Moment of Inertia of a Rod having non-uniform, linearly increasing mass density

Moment of Inertia of Rod having non-uniform, linearly increasing mass density Moment of Inertia Moment of inertia is of great importance when we come to discuss the rotational dynamics. The the word “inertia” refers to resistance against any change in state of object (mass). Specifically, the moment of inertia is measure of a body’s resistance […]

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head on collision in mechanics

A ball of mass m moving at a sped v makes a head on collision with an identical ball at rest. If the kinetic energy of the balls after collision is [latex]\frac34th[/latex] of the original. Then the coefficient of restitution is

Head on collision : Important case of partial elastic collision Q.A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest. If the kinetic energy of the balls after collision is of the original. Then the coefficient of restitution is (A) (B) (C) (D) Solution

A ball of mass m moving at a sped v makes a head on collision with an identical ball at rest. If the kinetic energy of the balls after collision is [latex]\frac34th[/latex] of the original. Then the coefficient of restitution is Read More »

What is the maximum compression in the spring, if the lower block is shifted to rightward with acceleration a. (Given that all surfaces are smooth as shown).

What is the maximum compression in the spring, if the lower block is shifted to rightward with acceleration a. (Given that all surfaces are smooth as shown).

Maximum compression in the spring Q.What is the maximum compression in the spring, if the lower block is shifted to rightward with acceleration a. (Given that all surfaces are smooth as shown). (A) (B) (C) (D) Table of Contents Solution Let us assume that the upper block of mass ‘m’ displaces by distance ‘x’ towards

What is the maximum compression in the spring, if the lower block is shifted to rightward with acceleration a. (Given that all surfaces are smooth as shown). Read More »

static friction to move two blocks together for IIT-JEE and NEET

For given system of two blocks, find the maximum value of force F which can be applied on the system as shown in figure so that both blocks move together. [Given coefficient of static friction between both blocks = 0.3]

How Static Friction helps two blocks to move together ! Q.For given system of two blocks, find the maximum value of force F which can be applied on the system as shown in figure so that both blocks move together. [Given coefficient of static friction between both blocks = 0.3] (A) 3N (B) 6N (C)

For given system of two blocks, find the maximum value of force F which can be applied on the system as shown in figure so that both blocks move together. [Given coefficient of static friction between both blocks = 0.3] Read More »

Rolling of a solid disc on horizontal and its K.E. energies Mechanics 10 Important Problems for IIT-JEE and NEET

A solid disc is rolling without slipping on a horizontal ground as shown in figure. Its total kinetic energy is 150 J . What are its translational and rotational kinetic energies respectively?

Rolling of a solid disc on horizontal Rolling , specifically a pure rolling is a classic example of combined translational and rotational motion. While talking about the rolling of a  solid disc over horizontal ground, actually we are discussing a simple case of rolling. Pure rolling refers rolling without slipping. Thus, there is no presence

A solid disc is rolling without slipping on a horizontal ground as shown in figure. Its total kinetic energy is 150 J . What are its translational and rotational kinetic energies respectively? Read More »

Count of Beats : How to determine the frequency of Unknown Tuning Fork

Count of Beats: How to determine the frequency of Unknown Tuning Fork

Count of Beats : How to determine the frequency of Unknown Tuning Fork Beats is a popular word among musician. Using beats formation concept, they tune their instruments while playing them against some standard frequency. All instruments come into tune when beats disappear. Now the instruments sound with same standard frequency which implies that there has

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A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of water in the capillary tube is 4g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is:

A capillary tube of radius r is immersed in water and water rises in it to a height h . The mass of water in the capillary tube is 4g . Another capillary tube of radius 2 r is immersed in water. The mass of water that will rise in this tube is:

A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of water in the capillary tube is 4g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is: (A) 2g (B) 2.5g (C)

A capillary tube of radius r is immersed in water and water rises in it to a height h . The mass of water in the capillary tube is 4g . Another capillary tube of radius 2 r is immersed in water. The mass of water that will rise in this tube is: Read More »

A wooden ball of density [latex]900 kg / m^{3}[/latex] is immersed in a liquid of density [latex]1200 kg / m^{3}[/latex] to a depth of 126 cm and the released. The height h above the surface of which the ball rises will be

A wooden ball of density [latex]900 kg / m^{3}[/latex] is immersed in a liquid of density [latex]1200 kg / m^{3}[/latex] to a depth of 126 cm and the released. The height h above the surface of which the ball rises will be

A wooden ball of density is immersed in a liquid of density to a depth of 126 cm and the released. The height h above the surface of which the ball rises will be (A) 40 cm (B) 42 cm (C) 45 cm (D) 50 cm Solution Let = Volume of ball Given that, =

A wooden ball of density [latex]900 kg / m^{3}[/latex] is immersed in a liquid of density [latex]1200 kg / m^{3}[/latex] to a depth of 126 cm and the released. The height h above the surface of which the ball rises will be Read More »

A block of mass 1 kg and density 0.8 [latex]g/cm^3[/latex] is held stationary with the help of a string as shown in figure. The block is completely immersed into the water filled in tank.If the tank is accelerating vertically upwards with an acceleration a = 2[latex]m/s^2[/latex]. Find the tension in the string.

A block of mass 1 kg and density 0.8 [latex]g/cm^3[/latex] is held stationary with the help of a string as shown in figure. The block is completely immersed into the water filled in tank.If the tank is accelerating vertically upwards with an acceleration a = 2[latex]m/s^2[/latex]. Find the tension in the string.

A block of mass 1 kg and density 0.8 is held stationary with the help of a string as shown in figure. The block is completely immersed into the water filled in tank.If the tank is accelerating vertically upwards with an acceleration a = 2 (i) Find the tension in the string. (A) 3 N

A block of mass 1 kg and density 0.8 [latex]g/cm^3[/latex] is held stationary with the help of a string as shown in figure. The block is completely immersed into the water filled in tank.If the tank is accelerating vertically upwards with an acceleration a = 2[latex]m/s^2[/latex]. Find the tension in the string. Read More »

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