Physics Laws of Motion

When a body slides down from rest along a smooth inclined plane making an angle of 30° with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and though the same distance, it takes time aT, where a is a constant greater than 1. The co-efficient of friction between the body and the rough plane is   $\frac{1}{\sqrt[]{x}}\left(\frac{{\alpha }^2-1}{\alpha }\right)$ where x =___________.

Statement-I: Two forces $\left(\overrightarrow{P}+\overrightarrow{Q}\right)and\left(\overrightarrow{P}-\overrightarrow{Q}\right)where\overrightarrow{P}\perp \overrightarrow{Q},$ when act at an angle θ₁ to each other the magnitude of their resultant is $\sqrt[]{3\left(P^2+Q^2\right)},$ when they act an angle θ₂, the magnitude of their resultant becomes $\sqrt[]{2\left(P^2+Q^2\right)}.$ This is possible only when θ₁ < ₂.

Statement-II: In the situation given above.

θ₁ = 60° and θ₂ = 90°

In the light of the above statements, choose the most appropriate answer from the options given below:-

A block of mass m slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is: Given m = 8 kg, M = 16kg. Assume all the surfaces shown in the figure to be frictionless.

Statement-I: If three forces ${\overrightarrow{F}}_1,{\overrightarrow{F}}_{2}and{\overrightarrow{F}}_3$  are represented by three sides of triangle and, ${\overrightarrow{F}}_1+{\overrightarrow{F}}_2=-{\overrightarrow{F}}_3,$  then these three forces are concurrent forces and satisfy the condition for equilibrium.

Statement-II: A triangle made up of three forces ${\overrightarrow{F}}_1,{\overrightarrow{F}}_{2}and{\overrightarrow{F}}_3$  as its sides taken in the same order, satisfy the condition for translator equilibrium.

In the light of the above statements, choose the most appropriate answer from the options given below:

A body of mass M moving at speed V₀ collides elastically with a mass 'm' at rest. After the collision, the two masses move at angles q₁ and q₂ with respect to the initial direction of motion of the body of mass M. The largest possible value of the ratio M/m, for which the angles q₁ and q₂ will be equal, is:

A car is moving on a plane inclined at 30° to the horizontal with an acceleration of 10ms^-2 parallel to the upward. A bob is suspended by a string from the roof of the car. The angle in degree which the string makes with the vertical is______. (Take g = 10ms^-2)

The boxes of masses 2kg and 8kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8kg to strike the ground starting from rest. (use g = 10 m/s²)

The resultant of these forces $\overrightarrow{OP},\overrightarrow{OQ},\overrightarrow{QR},\overrightarrow{OS}and\overrightarrow{OT}$  is approximately. . . . . . .N

[Take $\sqrt[]{3}=1.7,\sqrt[]{2}=1.4.$  Given $\widehat{i}and\widehat{j}$  unit vectors along x, y axis]

A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega .$  The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$ . The beaker will revolve with the disc if :

Why is the First Law of Motion important?