Overview

Two billiard balls of equal mass 30g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and ball 'b' by the wall along 'X' direction is :
(Diagram shows ball 'a' hitting the wall perpendicularly along the x-axis and ball 'b' hitting the wall at a 45° angle to the x-axis.)

An inclined plane in bent in such a way that the vertical cross-section is given by y  where y is in vertical and x in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction = 0.5, the maximum height in cm at with a stationary block with not skip downward is ____________cm.

The coefficient of static friction between a wooden block of mass 0.5kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall be__________ N.

A person standing on a balance inside a stationary lift measures 60 kg. The weight of that person if the lift descends with uniform downward acceleration of 1.8m/s² will be----------N. [g = 10 m/s²]

As shown in the figure, a block of mass $\sqrt[]{3}kg$ is kept on a horizontal rough surface of coefficient of friction $\frac{1}{3\sqrt[]{3}}.$ The critical force to be applied on the vertical surface as shown at an angle 60° with horizontal such that it does not move, will be 3x. The value of x will be-------------.

[g = 10m/s² ; sin 60° = $\frac{\sqrt[]{3}}{2};$ cos60° = $\frac{1}{2}]$

A boy pushes a box of mass 2kg with a force $\overrightarrow{F}=\left(20\widehat{i}+10\widehat{j}\right)N$ on a frictionless surface. If the box was initially at rest, then-------------m is displacement along the x – axis after 10s.

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Body 'P' having mass M moving with speed 'u' has head – on collision elastically with another body 'Q' having mass  'm' initially at rest. If m << M, Body 'Q' will have a maximum speed equal to '2u' after collision.

Reason R : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below

Two particles having masses 4g and 16g respectively are moving with equal kinetic energies. The ratio of the magnitudes of their linear momentum is n : 2. The value of n will be……….

Three masses M = 100kg, m₁ = 10kg and M₂ = 20kg are arranged in a system as shown in figure. All the surface are frictionless and strings are inextensible and weightless. The pulleys are also weightless and frictionless. A force F is applied on the system so that the mass m₂ moves upward with an acceleration of 2ms^-2. The value of F is:

(Take g = 10ms^-2)

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: