If the unit of length,mass and force are chosen as fundamental units, the dimensions of time would be:
(Given F = )a/t) + bt2, where F denotes force and t time. The dimensions of a and b are respectively:
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A student measures the distance traversed in free fall a body initially at rest in a given time. He uses this data to estimate g, the acceleration due o gravity. If the maximum percentage errors in the measurement of distance and time are e1 and e2 respectively, the percentage error in the measurement of g is :
The velocity versus time graph of a body moving in a straight line is shown in fig. The displacement of the body in 5 s is:
A projectile is fired at 300 with momentum p. Neglecting air friction, the change n kinetic energy when it returns to the ground will be:
A monkey is descending fromthe branch of a tree with acceleration. If the breaking strength of the branch is 75% of the weight of the monkey, the minimum acceleration with which monkey can slide down without breaking the branch is:
The coefficient of static friction ( s) between block A of mass 2 kg and the table as shown in Fig. is 0.1. What would be the maximum mass of block B so that the two blocks do not move ? The string and the pulley are assumed to be smooth and mass less (g = 10 m/s2):
Two inclined frictionless tracks, one gradual and the steepmeet at A from where two stones are allowed to slide down from rest, one on each track, as shown in Fig. Which of the following statement is correct ?
Two trucks, one loaded (A) and the other unloaded (B) moving and have same kinetic energy. The mass of A is double that of B.Brakes are applied to both and are brought to rest. If the distance covered by A before coming to rest is x1 and that of B is x2 , then:
The total work done on a particle is equal to the change in kinetic energy
A disc of moment of inertia I1 is rotating with an angular velocity ω1.Another disc of moment of inertia I2 which is not rotating, is gently put on the first disc. The angular speed of the system will be:
Two circular discs of same mass and thickness are made from metals having densities ρ1 and ρ2 respectively. The ratio of their moments of inertia a out the central axis perpendicular to the plane of the disc will be:
A tangential force F acts along the a ring of radius R and displace the ring through and angle θ . The work done by the force is :
If there are no heat losses, the heat released by the condensation of x gram of steam at 1000C into water at 1000C can be used to convert y gram of ice at 00C into water at 1000C. The ratio y : x is nearly
Steam at 1000C is passed into 1.1 kg of water contained in a calorimeter of water equivalent 0.02 kg at 150C till the temperature of the calorimeter rises to 800C . The mass of condensed in kg, is:
An aluminium sphere of 20cm diameter is heated from 00C to 1000C. Its volume changes by : (Given that coefficient of linear expansion for aluminium, αAl = 23 x 10-6/0C)
Two identical disks are positioned on a vertical axis shown in the figure. The bottom disk is rotating at an angular velocity ω0 and has rotational kinetic energy k0. The top disk is initially at rest. It allowed to fall and sticks to the bottom disk The change in the rotational kinetic energy of the system after the collision is:
An ideal monoatomic gas undergoes a process given by P = 3V2. Then
An ideal gas heat engine operates in a Carnot cycle be ween 227ºC and 127ºC. It absorbs 6 kcal at the higher temperature. The amount of heat ( n kcal) converted into work is equal to :
In a given process on an ideal gas, dW = 0 and dQ < 0 Then for the gas
Whenthe net force F acting on the particle varies as its position along x-axis shown in the figure, which of the following cannot be oscillatory motion. (where position of the particle)
A physical quantity A is related to four observables a,b,c and d as : A = a2b3/ √c d . The percentage errors of measurements in a,b,c and d are 1%, 32%, 2%and2%respectively.What is the percentage error in the quantity A ?
The acceleration a of a particle starting from rest varies with time according to relation : a = αt + β. The velocity of the particle after a time t will be:
If two stones projected from the same point with the same speed but at angle π/3 and π/6 respectively have their ranges R2 and R1, then:
A ball is let fall from a height h0. There are n collisions with the Earth. If the velocity of rebound after n collisions is vn and the ball rises to a height hn , then coefficient of restitution is given by:
A rod of length L and mass M is bent to form a semicircular ring. The moment of inertia of the ring about is diameter is:
The figure given below show a process (relating pressure P and volume V) for a given amount for an ideal gas. W is work done by the gas and Q is heat absorbed by the gas
An ideal gas with pressure P volume V and temperature is expanded isothermally to a volume 2V and a final pressure Pi . If the same gas is expanded adiabatically to a volume 2V, the final pressure is Pa. The ratio of the specific heat of the gas is 1.67. The ratio is
Masses are suspended in vertical plane as shown (the system is at rest and in equilibrium). When m1 is removed the system makes 20 oscillations in 40 sec.When m2 is also removed gently then how long the system will take to complete 30 oscillations :
A particle of mass 10 gm is placed in a potential field given by V= (50 x2 + 100) J/kg. The frequency of oscillation in cycle/sec is :