A ball is given some velocity at a and moves along a semicircular ring fixed on a smooth horizontal table the dotted line shows the path of the marble.the marble will leave the ring in which direction​ 1,2 or 3 the marble will leave the ring?

Street Plan : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All other streets of the city run parallel to these roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent roads/ streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : the 2^(nd) street running in the North -South direction and 5^(th) in the East - West direction meet at some crossing, then we will call this crossstreet (2, 5). Using this convention find : how many cross-streets can be referred to as (4, 3).

Street Plan : A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction. All other streets of the city run parallel to these roads and are 200 m apart. There are about 5 streets in each direction. Using 1 cm = 200 m, draw a model of the city on your notebook. Represent roads/ streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East - West direction. Each cross street is referred to in the following manner : the 2^(nd) street running in the North -South direction and 5^(th) in the East - West direction meet at some crossing, then we will call this crossstreet (2, 5). Using this convention find : how many cross-streets can be referred to as (3, 4).

A particle P starts from the point z_0=1+2i , where i=sqrt(-1) . It moves first horizontally away from origin by 5 units and then vertically away from origin by 3 units to reach a point z_1dot From z_1 the particle moves sqrt(2) units in the direction of the vector hat i+ hat j and then it moves through an angle pi/2 in anticlockwise direction on a circle with centre at origin, to reach a point z_2dot The point z_2 is given by

A wire of mass 9.8*10^(-3) kg per metre passes over a friction less pulley fixed on the top of an inclined friction less plane which makes an angle of 30^@ with the horizontal. Masses M_(1) and M_(2) are tied at the two end of the wire. The mass M_(1) rests on the plane and the mass M_(2) hangs vertically downward. The whole system is in equilibrium. Now a transverse wave propagates along the wire with a velocity of 100ms^(-1) . Find the values of masses M_(1) and M_(2) . Take g= 9.8ms^(-2) .

A solid disc and a ring, both of radius 10 cm are placed on a horizontal table simultaneously, with initial angular speed equal to 10 pi rad s^-1 . Which of the two will start to roll earlier ? The co-efficient of kinetic friction is mu_k=0.2 .