Part Test- 1 (JEE Main 2018) - JEE MCQ

Two masses m₁ and m₂ which are connected with a light string, are placed over a frictionless pulley. This set up is placed over a weighing machine, as shown. Three combination of masses m₁ and m₂ are used, in first  case m₁ = 6 kg and m₂ = 2 kg, in second case m₁ = 5 kg and m₂ = 3kg and in third case m₁ = 4 kg and m₂ = 4 kg.  Masses are held stationary initially and then released. If the readings of the weighing machine after the release in three cases are W₁, W₂ and W3 respectively then :

The ratio of work done by the internal forces of a car in order to change its speed from 0 to V and  from V to 2V is (Assume that the car moves on a horizontal road) -  

A weightless rod of length 2l carries two equal masses 'm', one tied at lower end A and  the other at the middle of the rod at B. The rod can rotate in vertical plane about a fixed horizontal axis passing through C. The rod is released from rest in horizontal position. The speed of the mass B at the instant rod, become vertical is :

Power versus time graph for a given force is given below. Work done by the force upto time t(<t₀).

A motor car is going due north at a speed of 50 km/h. It makes a 90º left turn without changing the speed. The change in the velocity of the car is about 

A body is thrown horizontally with a velocity  from the top of a tower of height h. It strikes the level ground through the foot of the tower at a distance x from the tower. The value of x is

A train is standing on a platform , a man inside a compartment of a train drops a stone . At the same instant train starts to move with constant acceleration . The path of the particle as seen by the person who drops the stone is :

P is a point moving with constant speed 10 m/s such that its velocity vector always maintains an angle 60° with line OP as shown in figure (O is a fixed point in space). The initial distance between O and P is 100 m. After what time shall P reach O.

A mosquito with 8 legs stands on water surface and each leg makes depression of radius ' a'. If the surface tension and angle of contact are ' T '  and  zero  respectively , then the weight of mosquito is :

The work done in increasing the size of a rectangular soap film with dimensions 8 cm × 3.75 cm to 10 cm × 6 cm is 2 × 10^–4 J. The surface tension of the film in N/m is :  

The property of surface tension is to :    

Two uniform rods of equal length but different masses are rigidly joined to form a L-shaped body, which is then pivoted about O as shown. If in equilibrium  the body is in the shown configuration, ratio M/m will be:

A large open tank has two small holes in its vertical wall as shown in figure. One is a square hole of side 'L' at a depth '4y' from the top and the other is a circular hole of radius 'R' at a depth ‘y’ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then, 'R' is equal to :

A stationary body explodes into two fragments of masses m₁ and m₂. If momentum of one fragment is p, the energy of explosion is : 

A shell of mass 2 m projected with a speed ' u ' at an angle θ to the horizontal explodes at the highest point of its motion into two pieces of mass ' m ' each. If one piece whose initial speed is zero, falls vertically, the distance at which the other piece will fall from the gun is given by :

A man of 80 kg attempts to jump from a small boat of mass 40 kg on to the shore. He can generate a relative velocity of 6 m/s between himself and boat. His velocity towards the shore is : 

A block of mass m slides along the track with coefficient of kinetic friction μ. A man pulls the block through a rope which makes an angle θ with the horizontal as shown in the figure. The block moves  with constant speed V. Power delivered by the man is :

A conical pendulum consists of a simple pendulum moving in a horizontal circle as shown in the figure. C is the pivot, O is the centre of the circle in which the pendulum bob moves and ω the constant angular velocity of the bob. If  is the angular momentum about point C, then

A sphere of mass m and radius r is projected in a gravity free space with speed v. If coefficient of viscosity is 1/π  , the distance travelled by the body before it stops is :  

Two same masses are tied with equal lengths of strings and are suspended at the same fixed point. One mass is suspended freely whereas another is kept in a way that string is horizontal as shown. This mass is given initial velocity u in vertical downward direction. It strikes the freely suspended mass elastically that is just able to complete the circular motion after the collision about point of suspension O. Magnitude of velocity u is :

A ring attached with a light spring is fitted in a smooth rod. The spring is fixed at the outer end of the rod. The mass of the ring is 3kg & spring constant of spring is 300 N/m. The ring is given a velocity ‘V’ towards the outer end of the rod  and the rod is set to be rotating with an angular velocity ω. Then ring will move with  constant speed with respect to the rod if :

A force  acts on a body due to which its position varies as   Work done by this force in initial 2 seconds is :  

A partical A is projected with speed V_A from a point making an angle 60º with the horizontal. At the same instant, a second particle B is thrown vertically upwards from a point directly below the maximum height point of parabolic path of A , with velocity V_B. If the two particles collide then the ratio of V_A/V_B should be : 

A uniform rod of density ρ, and length ‘l’ is having square cross-section of side ‘a’. It is placed in a liquid of equal density ρ vertically along length in a tank having sufficient height of liquid. The surface tension of liquid is ‘T’ and angle of contact is 120º. Then :

A rigid body undergoing uniform pure rolling encounters horizontal tracks AB and BC as shown in the figure AB is a smooth layer of ice and BC is a rough surface with μ = 1. Both AB & BC are rigid  tracks. Which of the following statements are correct:

    (1) the body will slow down over BC                                        
    (2) the body will start slipping on AB
    (3) the body remains in pure rolling over the whole stretch AC
    (4) the angular velocity of the body remains constant over the whole stretch AC.

A disc of mass m₀ rotates freely about a fixed horizontal axis through its centre. A thin cotton pad is fixed to its rim, which can absorb water. The mass of water dripping onto the pad is μ per second. After what time will the angular velocity of the disc get reduced to half of its initial value?

A uniform cylinder of mass M and radius R rolls without slipping down a slope of angle θ to the horizontal. The cylinder is connected to a spring constant K while the other end of the spring is connected to a rigid support at P. The cylinder is released when the spring is unstretched. The maximum distance that the cylinder travels is