A national roadway bridge over a canal is in the form of an arc of a circle of radius 49 m. What is the maximum speed with which a car can move without leaving the ground at the highest point? (Take g = 9.8 m/second square)
An athlete completes one round of a circular track of radius R in 40 sec. What will be his displacement at the end of 2 min. 20 sec
A body slides down a smooth curved track which is the quadrant of a circle having radius 10 m. The speed of the body at the bottom of the track is
A microscope has its main scale with 20 divisions in 1 cm and vernier scale with 25 divisions, the length of which is equal to the length of 24 divisions of main scale. The least count of microscope is:
25* vernier scale reading (vsd) = 24* main scale reading (msd)
1vsd = 0.96 msd
Least count = 1msd - 1vsd=1msd-0.96 msd = 0.04 msd
1 msd = 1/20 cm
So, least count
A gardener pushes a lawn roller through a distance of 20m. If he applies a force of 20 kg weight in a direction inclined at 60° to the ground, find the work done by him. (g=9.8m/s2)
F = 20kg wt = 20×9.8N
s = 20m
θ = 60°
W = Fscosθ = 20×9.8×20×cos60°
W = 1960J
A particle collides with another particle 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 (m/M= ratio of masses)
Answer :- a,d
Solution :- If nothing is given about the nature of collision, we can not presume it as perfectly elastic. Let e be the coefficient of restitution of collision. For inelastic collision e<1. The collision cannot be perfectly inelastic because the particles do not stick together after collision.
Just after collision
Conservation of linear momentum yields
Since e=v'v (numerically)
Since e≤1, m/M≤1
Hence a and d are correct.
One kilometer is equal to how many miles?
If two numerically equal forces P & P acting at a point produce a resultant force of magnitude P itself, then the angle between the two original forces is
The angular velocity (in rad/s) of a body rotating at N r.p.m. is
Angular velocity is defined as the rate of change of angular displacement with respect to time. It is usually expressed by a Greek letter ω (omega).
Mathematically, angular velocity,
If a body is rotating at the rate of N r.p.m. (revolutions per minute), then its angular velocity,
ω = 2πΝ / 60 rad/s
An object with a mass of 10kg moves at a constant velocity of 10m/s. A constant force then acts for 4 sec on the object and gives it a speed of 2m/sec in opposite direction. The acceleration produced in it is
Change in velocity
Time required is 4 seconds
Three blocks of masses M1,M2 & M3 are connected by mass-less strings as shown on a friction-less table. They are pulled with a forceT3=40 N. If M1=10kg, M2 = 6kg, M3 = 4kg then TensionT2 will be:
Collision between two carom coins is an example for
The density of material in CGS system of units is 4g/ cm2.In a system of units in which unit of lengths is 10 cm and unit of mass is 100 g, the value of density of material will be
A person is holding a bucket by applying a force of 10N. He moves a horizontal distance of 5m and then climbs up a vertical distance of 10m. Find the total work done by him
F = 10N, s = 5m, θ = 90°
Work done, W1=Fscosθ = 10×5×cos90° = 0
For vertical motion, the angle between force and displacement is 0°.
Here, F = 10N, s = 10m, θ=0°
Work done, W2=10×10×cos0 = 100J
Total work done = W1+W2 = 100J
On the basis of dimensional equation, the maximum number of unknown that can be found, is
Since we define the dimension of the physical quantity into three parameters- mass
Thus we can find maximum of three unknown on the basis of dimensional equation.
Two blocks of masses M = 5 kg and m = 3 kg are placed on a horizontal surface as shown in this Fig. The coefficient of friction between the blocks is 0.5 and that between the block M and the horizontal surface is 0.7 . What is the maximum horizontal force F that can be applied to block M so that the two blocks move without slipping ?Take g = 10 ms
Let F be the maximum horizontal force that can be applied to block M so that the two blocks move without slipping , i.e. block m doesn't move to backward position.
Lets say, the coefficient of frostion between surface and M is µ1 & that between M and m is µ2
When force F acts on the block combination, friction f acts in the opposite direction as shown in the fig above.
So, the acceleration of the combination
Because of this accelaration, a force F' = ma acts in the opposite direction of accelaration. For this the friction between m and M acts in the same direction of accelaration as shown below.
A particle is projected up a 45° rough incline with a velocity 'v'. The coefficient of friction is 0.5 the speed with which it returns back to the straight point is v1 then v1/v is
A stone is projected upwards from the top of a building with some initial speed and reaches the ground in 5 sec. Now it is allowed to fall with the same initial speed downwards and reaches the ground in 3 sec. If the stone is allowed to fall freely under gravity from the same point, it will reach the ground in
If radian correction is not considered in specific heat measurement. The measured value of specific heat will be
The two ends of a train moving with a constant acceleration pass a certain point with velocity u and v. The velocity with which the middle point of the train passes the same point is
A car travelling due north at 25 m/s turns west and travels at the same speed. The change in velocity is
If the sum of two unit vectors is also a unit vector, then the magnitude of their difference is
A person aims a gun at a bird from a point, at a horizontal distance of 100 m.If gun can impart a speed of 500m/s to the bullet,at what height above the bird must be aim his gun in order to hit it?(g = 10 ms-2)
Yes we can assume that a person is 100m horizontal distance away from the bird.
When the angular velocity of a uniformly rotating body has increased thrice, the resultant of forces applied to it increase by 60 N. Find the acceleration of the body in the two cases. The mass of the body, m = 3kg
In case of uniform circular motion which of the following physical quantities do not remain constant?
A parachutist of weight W strikes the ground with his legs fixed and comes to rest with an upward acceleration of magnitude 3g . force exerted on him by ground during landing is
A block of mass m is in contact with the cart C as shown. The coefficient of static friction between the block and cart is μ. The acceleration α of the cart that will prevent the block from falling satisfies
A satellite in force-free space sweeps stationary interplanetary dust at a rate (dM/dt) =αv. The acceleration of satellite is