A car moves uniformly along a horizontal sine curve y = a sin (x/α), where a and α are certain constants. The coefficient of friction between the wheels and the road is equal to k. At what velocity will the car ride without sliding?

A large tank filled with water to a height 'h' is to be emptied through a small hole at the bottom. The ratio of times taken for the level of water to fall from h to h/2 and from h/2 to zero is

A bullet of mass 2 g is having a charge of 2μC. The potential difference it must be accelerated through, starting from rest, to acquire a speed of 10 m/s is

A wire of length L and 3 identical cells of negligible internal resistance are connected in series. Due to the current, the temperature of the wire is raised by ΔT in a time t. A number of N similar cells are now connected in series with a wire of the same material and area of cross-section but of length 2L. The temperature of the wire is raised by the same amount ΔT in the same time . The value of N is

The intensity of the light coming from one of the slits in YDSE is double the intensity from the other slit. Find the ratio of maximum intensity to minimum intensity in the interference fringe pattern observed.

Consider α-particles, β-particles and γ- rays each having an energy of 0.5 MeV. In increasing order of penetrating powers, the radiations are

A battery is supplying power to a tape-recorder by cable of resistance of 0.02 Ω . If the battery is generating 50 W power at 5V, then power received by tape-recorder is :

A uniform rod of mass m and length ℓ is rotating with constant angular velocity ω about an axis which passes through its one end and perpendicular to the length of rod. The area of cross section of the rod is A and its Young's modulus is Y. Neglect gravity. The strain at the mid point of the rod is :

Initially car A is 10.5 m ahead of car B. Both start moving at time t = 0 in the same direction along a straight line. The velocity time graph of two cars is shown in figure. The time when the car B will catch the car A, will be ;

Two masses m₁ and m₂ are connected by a string of length l. They are held in a horizontal plane at a height H above two heavy plates A and B made of different material placed on the floor. Initially distance between two masses is a < l. When the masses are released under gravity they make collision with A and B co - efficient of restitution 0.8 and 0.4 respectively. The time after the collision when the string becomes tight is