Govt. Exams
Entrance Exams
Elastic PE = ½kx² = ½ × 100 × (0.1)² = ½ × 100 × 0.01 = 0.5 J.
When a block slides down a frictionless incline, gravity's component along the slope determines the acceleration.
On an incline, gravity acts vertically downward, but only its component parallel to the slope causes acceleration down the incline.
Using F = ma, the net force along the incline equals mass times acceleration. The mass cancels out, giving us a pure kinematic result.
The acceleration down the incline is 4.9 m/s² (Answer: A)
Initial KE = ½m(v)² + ½m(2v)² = 2.5mv². Final velocity = 3v/2 (by momentum conservation). Final KE = ½(2m)(3v/2)² = 2.25mv²/4 = 0.84mv². Loss = 2.5 - 0.84 = 1.66, which is 2/3 of initial KE.
Electric field at surface: E = kQ/r² = (9 × 10⁹ × 8 × 10⁻⁶)/(0.02)² = (72)/(4 × 10⁻⁴) = 1.8 × 10⁷ N/C.
Wavelength λ = v/f = 1500/(50 × 10³) = 1500/50000 = 0.03 m = 3 cm. Higher frequencies in denser mediums produce shorter wavelengths.
Maximum velocity in SHM: v_max = ωA = 2πfA = 2π × 2 × 5 = 20π cm/s ≈ 62.8 cm/s.
After 30 years = 3 half-lives: N = N₀ × (1/2)³ = N₀/8. The sample reduces by half three times successively.
This problem involves using trigonometry to find the height of a ladder against a wall.
The ladder, wall, and ground form a right triangle where the ladder is the hypotenuse, the wall height is the opposite side to the 60° angle, and the ground distance is the adjacent side.
Since we need the height (opposite side) and have the hypotenuse and angle, we use the sine function: sine of the angle equals opposite divided by hypotenuse.
Substitute the value of sin(60°) = √3/2 and solve for height.
Calculate the approximate decimal value: 5√3 ≈ 5 × 1.732 = 8.66 m
The ladder reaches a height of 5√3 m or approximately 8.66 m on the wall.
Answer: (B) 5√3 m or 8.66 m
Object at 2f (40 cm = 2 × 20 cm) forms image at 2f. Using mirror equation confirms v = 40 cm, m = -1 (real, inverted, same size as object).
Each half has resistance R/2. When connected in parallel: 1/R_new = 1/(R/2) + 1/(R/2) = 4/R, so R_new = R/4.