Overview

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:

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 initial mass of a rocket is 1000kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20ms^-2. The gases come out at a relative speed of 500ms^-1 with respect to the rocket: [Use g = 10m/s²]

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 $\omega .$ The beaker will revolve with the disc if :

For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions. What additional forces must be applied and at what angle with positive x-axis so that the net acceleration of body is zero?

Two billiard balls of mass 0.05 kg each moving in opposite directions with 10ms^-1 collide and rebound with the same. If the time duration of contact is t = 0.005s. Then what is the force exerted on the ball due to each other?

A drop of liquid of density $\rho$  is floating half immersed in a liquid of density $\sigma$  and surface tension 7.5 * 10^-4Ncm^-1. The radius of drop in cm will be: (g = 10ms^-2)

A balloon has mass of 10g in air. The air escapes from the balloon at a uniform rate with velocity 4.5 cm/s. If the balloon shrinks in 5s completely. Then, the average force acting on the balloon will be (in dyne).