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A ball of mass 0.5 kg moving with a velocity of 2 m/s strikes a wall normally and bounces back with the same speed. If the time of contact between the ball and the wall is one millisecond, the average force exerted by the wall on the ball is

1) 2000 N 2) 1000 N 3) 5000 N 4) 125 N Answer: 1) 2000 N Solution: Force = change in momentum/time = [0.5 x 2 - (-2 x 0.5)]/10-3 F =... View Article

A force of 20 N is applied on a body of mass 5 kg resting on a horizontal plane. The body gains kinetic energy of 10 joules after it moves a distance of 2 m. The frictional force is

1) 10 N 2) 15 N 3) 20 N 4) 30 N Answer: 2) 15 N Solution: Given, Force, F = 20 N Mass of the body, m = 5 kg Kinetic energy = 10 J... View Article

A motorcyclist of mass m is to negotiate a curve of radius r with a speed v. The minimum value of the coefficient of friction so that this negotiation may take place safely is

1) v2rg 2) v2/gr 3) gr/v2 4) g/v2r Answer: 2) v2/gr Solution: The frictional force is balanced by the centrifugal force f =... View Article

A car turns a corner on a slippery road at a constant speed of 10 m/s. If the coefficient of friction is 0.5, the minimum radius of the arc in meter in which the car turns is

1) 20 2) 10 3) 5 4) 4 Answer: 1) 20 Solution: Given, v = 10 m/s coefficient of friction, μ= 0.5 We know that vmax... View Article

A block moving on a surface with a velocity of 20 ms^-1 comes to rest because of surface friction over a distance of 40 m. The coefficient of dynamic friction is (take, g =10 ms^-2)

1) 0.5 2) 0.3 3) 0.2 4) 0.1 Answer: Given, Velocity,u = 20 m/s Distance, s= 40 m v2 = u2 + 2as ⇒ 0 = (20)2 + 2(μg)(40)... View Article

A body is coming with a velocity of 72 km/h on a rough horizontal surface with a coefficient of friction of 0.5. If the acceleration due to gravity is 10 ms^-2, find the minimum distance, it can be stopped.

1) 400 m 2) 40 m 3) 0.40 m 4) 4 m Answer: 2) 40 m Solution: Velocity of the body, u= 72 x 5/18 = 20 m/s coefficient of friction of... View Article

Gist of EPW September Week 4, 2021

The Economic and Political Weekly (EPW) is an important source of study material for IAS, especially for the current affairs segment. In this... View Article

Find ten rational numbers between -2/5 and 1/7.

Solution: A number that can be expressed as p/q, where q is not equal to zero is called a rational number. Given numbers are -2/5 and 1/7. LCM... View Article

Factorise 27x³ + y³ + z³ – 9xyz

Solution: 27x3 + y3 + z3 - 9xyz = (3x)3 + y3 + z3 - 9xyz = (3x)3 + y3 + z3 - 3×3x × y × z Use identity a3 + b3 + c3 - 3abc =... View Article

What is the period of the function f(x) = sin x.

(a) π (b) π/2 (c) 2π (d) π/2 Solution: The period of the function f(x) = sin x is 2π. Hence option c is the answer.... View Article

Find two rational numbers between -3 and -2.

A number which can be expressed as p/q, where q not equal to zero is called a rational number. Use formula x = (a+ b)/2 => (-3 + -2)/2 =... View Article

Integrate the function x tan^-1 x.

Solution: We use product rule of integration. ∫ f(x). g(x) dx = f(x) ∫ g(x)- ∫ f’(x) ∫g(x) dx Take tan-1 x as first... View Article

Rohan’s mother is 26 years older than him. The product of their ages 3 years from now will be 360. Find Rohan’s present age.

Answer: Let x be the present age of Rohan. Mother’s age = x + 26 Age of Rohan after 3 years = x + 3 Age of mother after 3 years =... View Article

What is the angle name for half a revolution?

Solution: Half a revolution is called a straight angle. So straight angle is the angle name for half a revolution. The straight angle is 1800.... View Article

Prove that tan(x – y) = (tan x – tan y)/(1 + tan x tany)

Solution: LHS = tan(x - y) = sin (x - y)/cos (x - y) sin (x - y) = (sin x cos y - cos x sin y) cos (x - y) = (cos x cos y + sin x sin y) sin... View Article

The value of 101³ is

(a) 1030301 (b) 1000301 (c) 10303001 (d) 10300301 Solution: (101)3 = (100 + 1)3 Use identity (a + b)3 = a3 + 3a2b + 3ab2 + b3 (100 + 1)3 =... View Article

In a hospital, used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of hospital whose length is 25 m and breadth is 20 m. If tank is filled completely then what will be the height of standing water used for irrigating the park.

Solution: Diameter of cylindrical tank = 2m So radius, r = 2/2 = 1 m Height of cylindrical tank, H = 5 m Volume of tank = πr2h =... View Article

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