A school bus picking up children in a colony of flats stops at every sixth block of flats. Another school bus starting from the same place stops at every eighth blocks of flats. Which is the first bus stop at which both of them will stop?

A particle of mass m collides with another stationary particle of mass M such that the second particle starts moving and the first particle stops just after the collision. Then which of the following conditions must always be valid ?

A block is pushed with some velocity up a rough inclined plane. It stops after ascending few meters and then reverses its direction and returns back to point from where it started. If angle of inclination is 37^(@) andthe time to climb up is half of the time to return back then coefficient of friction is:

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line (see Figure). A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run? [Hint : To pick up the first potato and the second potato, the total distance (in metres) rim by a competitor is 2 x 5 + 2 x (5 + 3)]

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line (see Figure).A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?[Hint : To pick up the first potato and the second potato, the total distance (in metres) rim by a competitor is 2 x 5 + 2 x (5 + 3)]

A plank of mass M and length L is placed at rest on a smooth horizontal surface. A small block of mass m is projected with a velocity v_0 from the left end of it as shown in figure. The coefficient of friction between the block and the plank is m, and its value is such that the block becomes stationary with respect to the plank before it reaches the other end. a. Find the time and common velocity when relative sliding between the block and the plank stops. b. Find the work done by the friction force on the block during the period it slides on the plank. Is the work positive or negative? c. Calculate the work done on the plank during the same period. Is the work positive or negative? d. Also, determine the net work done by friction, Is it positive or negative?

In a hexagonal system system of crystals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are regular hexagons, and three atoms are sandwiched in between them. A space-cilling model of this structure, called hexagonal close-packed is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spheres are then placed overt the first layer so that they touch each other and represent the second layer so that they touch each other and present the second layer. Each one of the three spheres touches three spheres of the bottom layer. Finally, the second layer is converted with a third layer identical to the bottom layer in relative position. Assume the radius of every sphere to be r . The number of atom in this hcp unit cell is (a)4 (b)6 (c)12 (d)17

In a hexaonal system system of cycstals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are refular hexagons, and three atoms are sandwiched in between them. A space-cilling model of this structure, called hexagonal close-paked is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spherres are then placed overt the first layer so that they toych each other and represent the second layer so that they toych each other and present the second layer. Each one of the three spheres touches three spheres of the bottom layer. Finally, the second layer is convered with a third layer identical to the bottom layer in relative position. Assume the radius of every sphere to be r . The empty space in this hcp unit cell is (a) 74% (b) 48.6% (c) 32% (d) 26%

In a hexaonal system system of cycstals, a frequently encountered arrangement of atoms is described as a hexagonal prism. Here, the top and bottom of the cell are refular hexagons, and three atoms are sandwiched in between them. A space-cilling model of this structure, called hexagonal close-paked is constituted of a sphere on a flat surface surrounded in the same plane by six identical spheres as closely as possible. Three spherres are then placed overt the first layer so that they toych each other and represent the second layer so that they toych each other and present the second layer. Each one of the three spheres touches three spheres of the bottom layer. Finally, the second layer is convered with a third layer identical to the bottom layer in relative position. Assume the radius of every sphere to be r . The number of atom in this hcp unit cell is