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A particle moving along x-axis has an acceleration f at time t, given by [latex]f = f_{0}(1-frac{t}{T})[/latex], where [latex]f_{0}[/latex] and T are constants. The particle at T = 0 has zero velocity. In the time interval between t = 0 and the instant when f = 0, the velocity (v_a) of the particle is then:(a) [latex]frac{1}{2}f_{0}T[/latex](b) [latex]f_{0}T[/latex](c) [latex]frac{1}{2}f_{0}T^{2}[/latex](d) [latex]f_{0}T^{2}[/latex]

Given \(\begin{array}{l}f = f_{0}(1-\frac{t}{T})\end{array} \) where \(\begin{array}{l}f_{0}\end{array} \) and T are constants At t = 0 and v = 0... View Article

A wheel has angular acceleration of 3.0 rad/s^2 and an initial angular speed of 2.00 rad/s. In a time of 2 s it has rotated through an angle (in radian) of: (A) 6 (B) 12 (C) 10 (D) 4

Answer: (C) 10 Solution: Initial angular speed, ω0 =2 rad/s Angular acceleration, α=3 rad/s2 t = 2s Hence, θ=ω0t+ 1/2αt2 = 2 x... View Article

Acceleration of a projectile relative to another projectile is:

The acceleration of a projectile relative to another projectile is zero. It is because both the particles will have the... View Article

A particle has initial velocity (2i+3j) and acceleration (0.3i+0.2j) the magnitude of the velocity after 10 second will be: (a) 9√2 units (b) 5√2 units (c) 5 units (d) 9 units

Answer: (b)5√2 Given, u = 2i + 3j a = 0.3i + 0.2j t = 10s As, v = u... View Article

What is the moment of inertia of a solid sphere of density ρ and radius R about its diameter? (A) (105 / 176) R^5ρ (B) (176 / 105) R^5ρ (C) (105 / 176) R^2ρ (D) (176 / 105) R^2ρ

Answer: (B) (176/105) R5ρ Solution: For sphere MI = (2/5)MR2 Density = [(mass) / (volume)] hence ρ = (M /... View Article

The height y nad the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y = (8t – 5t^2) m and x = 6t m, where t is in seconds. The velocity with which the projectile is projected at t = 0 is.

y = 8t – 5t2 Differentiating both the sides w.r.t. t dy/dt = 8 – 10t Vy = 8 –... View Article

Two particles X and Y having equal charges after being accelerated through same potential difference enter a region of uniform magnetic field and describe a circular paths of radii ‘r1’ and ‘r2’ respectively. The ratio of the mass of X to that of Y is:

Since, Magnetic Force = qVB and Centripetal force = (mV2/r) Hence, [(mV2)/r] = qVB So, r = (mV/qB) Thus, mV = qrB ………(i)... View Article

Simplify: 1/8-(1/6-1/4)

(1/8)-[(1/6-1/4)] = 1/8 – (4-6)/24 = 1/8 + 2/24 = (3+2)/24 = 5/24

Observe the pattern and fill in the blanks: (i) 2,4,6,8,…. (ii) 1,3,6, 10,…. (iii) 9, 109, 209,_,_,___

(i) 2,4,6,8,10,12,14. (ii) 1, 3, 6, 10, 15, 21, 28, 36, 45. (iii) 9, 109, 209,309,409,509

Solve the equation and check your results: (2x/3)+1=(7x/15)+3

Given, (2x/3)+1=(7x/15)+3 \(\begin{array}{l}\frac{2 x}{3}-\frac{7 x}{15}=3-1 \\ \frac{10 x-7 x}{15}=2 \\ \frac{3 x}{15}=2\end{array} \) Therefore, x = 10 Verification: Putting x... View Article

Find the mean of first five composite number

The first five composite numbers are: 4, 6, 8, 9, 10 As we know, Mean = (Sum of values)/(Total number of... View Article

In simple Regression equation the number of variables involved are: (a)2 (b)1 (c) 0 (d) 3

Answer: (a) 2 A linear regression is represented as: y = a + bx, where x and y are variables.

Solve the following equation: 3(t – 3) = 5 (2t + 1).

3(t−3) = 5(2t+1) 3t − 9 = 10t + 5 3t – 10t = 5 + 9 -7t = 14... View Article

In euclids division lemma when a=bq+r where a,b are positive integers then what values r can take?

Answer: 0 ≤ r < b According to Euclid’s Division Lemma if we have two positive integers a and b,... View Article

Find the ratio of 5m to 10km

Given, 5m to 10km 10 km = 10 x 1000 = 10000 m 5m/10km = 5m/10000m = 1/2000 = 1:2000

List the alphabets having rotational symmetry and reflection symmetry, also list the orders in rotational symmetry as well as reflections symmetry.

Alphabets having a reflection symmetry about a vertical mirror are A, H,I, M, O, T, U, V, W, X, Y... View Article

A fruit-seller had some apples. He sells 40% of them and still has 420 apples. Find the number of apples he had originally.

Assume that the fruit seller initially had 100 apples He sell 40% of them = 40 apples Left out apples... View Article

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