Variant 1 1 Length of a pendulum is equal to 7,31pm 0,62 Find relative error. Express the answer in terms of percentages. Round the answer to hundredths. 2 How will the volume of the cylinder increase with an increase in the radius of the base by 4 times and the height by 6 times? 4 How should the mass of a mathematical pendulum be changed so that its oscillation frequency increases by 2 times? A) increase by 4 times B) decrease by 2 times C) decrease by 4 times D) increase by 2 times E) nothing needs to be changed 3 In free fall, how much will the speed of the falling body increase in 12 seconds of falling? 5. A thrown body expiriences weightlessness __ a)at the maximum height b)never c)during all its flight

Question

Variant 1 1 Length of a pendulum is equal to 7,31pm 0,62 Find relative error. Express the answer in terms of percentages. Round the answer to hundredths. 2 How will the volume of the cylinder increase with an increase in the radius of the base by 4 times and the height by 6 times? 4 How should the mass of a mathematical pendulum be changed so that its oscillation frequency increases by 2 times? A) increase by 4 times B) decrease by 2 times C) decrease by 4 times D) increase by 2 times E) nothing needs to be changed 3 In free fall, how much will the speed of the falling body increase in 12 seconds of falling? 5. A thrown body expiriences weightlessness __ a)at the maximum height b)never c)during all its flight

Answer 1

1. The relative error is calculated as the absolute error divided by the measured value. In this case, the absolute error is 0.62 and the measured value is 7.31. So, the relative error is 0.62/7.31 = 0.0848. To express this as a percentage, we multiply by 100, giving a relative error of 8.48%. Rounding to the nearest hundredth, the relative error is 8.48%.2. The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height. If the radius is increased by 4 times and the height is increased by 6 times, the new volume will be V' = π(4r)^2(6h) = 96πr^2h. This is 96 times the original volume, so the volume of the cylinder will increase by 96 times.3. The frequency of oscillation of a mathematical pendulum is given by the formula f = 1/2π√(g/L), where g is the acceleration due to gravity and L is the length of the pendulum. If we want to increase the frequency by 2 times, we need to decrease the length of the pendulum by 4 times. So, the correct answer is C) decrease by 4 times.4. In free fall, the speed of a falling body increases by g (acceleration due to gravity) every second. So, in 12 seconds, the speed will increase by 12g. The exact value of g is approximately 9.8 m/s^2, so the speed will increase by 12*9.8 = 117.6 m/s.5. A thrown body experiences weightlessness during all its flight. This is because the force of gravity acting on the body is constant and does not change during the flight. So, the correct answer is c) during all its flight.

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